1.3.1 Kirchhoff’s Laws

Kirchhoff’s Laws relate to the algebraic sum of currents at a junction (or node) or voltages in a network (or mesh). The term “algebraic” simply indicates that the polarity of each current or voltage drop must be taken into account by giving it an appropriate sign, either positive (+) or negative (−).

Kirchhoff’s Current Law states that the algebraic sum of the currents present at a junction (node) in a circuit is zero (see Figure 1.66).

1.3.2 The Potential Divider

The potential divider circuit (see Figure 1.73) is commonly used to reduce voltages in a circuit. The output voltage produced by the circuit is given by:

It is, however, important to note that the output voltage (V_out) will fall when current is drawn from the arrangement.

Figure 1.74 shows the effect of loading the potential divider circuit. In the loaded potential divider (Figure 1.74) the output voltage is given by:

where:

1.3.3 The Current Divider

The current divider circuit (see Figure 1.76) is used to divert a known proportion of the current flowing in a circuit. The output current produced by the circuit is given by:

It is, however, important to note that the output current (I_out) will fall when the load connected to the output terminals has any appreciable resistance.

1.3.4 The Wheatstone Bridge

The Wheatstone bridge forms the basis of a number of useful electronic circuits including several that are used in instrumentation and measurement.

The basic form of Wheatstone bridge is shown in Figure 1.78. The voltage developed between A and B will be zero when the voltage between A and Y is the same as that between B and Y. In effect, R₁ and R₂ constitute a potential divider as do R₃ and R₄.

The bridge will be balanced (and V_AB = 0) when the ratio of R₁:R₂ is the same as the ratio R₃:R₄.

Hence, at balance:

A practical form of Wheatstone bridge that can be used for measuring unknown resistances is shown in Figure 1.79.

In this practical form of Wheatstone bridge, R₁ and R₂ are called the ratio arms while one arm (that occupied by R₃ in Figure 1.78) is replaced by a calibrated variable resistor. The unknown resistor, R_x, is connected in the fourth arm. At balance:

1.3.5 Thévenin’s Theorem

Thévenin’s Theorem allows us to replace a complicated network of resistances and voltage sources with a simple equivalent circuit comprising a single voltage source connected in series with a single resistance (see Figure 1.70).

The single voltage source in the Thévenin equivalent circuit, V_oc, is simply the voltage that appears between the terminals when nothing is connected to it. In other words, it is the open-circuit voltage that would appear between A and B.

The single resistance that appears in the Thévenin equivalent circuit, R, is the resistance that would be seen looking into the network between A and B when all of the voltage sources (assumed perfect) are replaced by short-circuit connections. Note that if the voltage sources are not perfect (i.e., if they have some internal resistance) the equivalent circuit must be constructed on the basis that each voltage source is replaced by its own internal resistance.

Once we have values for V_oc and R, we can determine how the network will behave when it is connected to a load (i.e., when a resistor is connected across the terminals A and B).

1.3.6 Norton’s Theorem

Norton’s Theorem provides an alternative method of reducing a complex network to a simple equivalent circuit. Unlike Thévenin’s Theorem, Norton’s Theorem makes use of a current source rather than a voltage source. The Norton equivalent circuit allows us to replace a complicated network of resistances and voltage sources with a simple equivalent circuit comprising a single constant current source connected in parallel with a single resistance (see Figure 1.85).

The constant current source in the Norton equivalent circuit, I_sc, is simply the short-circuit current that would flow if A and B were to be linked directly together. The resistance that appears in the Norton equivalent circuit, R, is the resistance that would be seen looking into the network between A and B when all of the voltage sources are replaced by short-circuit connections. Once again, it is worth noting that, if the voltage sources have any appreciable internal resistance, the equivalent circuit must be constructed on the basis that each voltage source is replaced by its own internal resistance.

As with the Thévenin equivalent, we can determine how a network will behave by obtaining values for I_sc and R.

1.3.7 C-R Circuits

Networks of capacitors and resistors (known as C-R circuits) form the basis of many timing and pulse shaping circuits and are thus often found in practical electronic circuits.

1.3.8 Charging

A simple C-R circuit is shown in Figure 1.91. In this circuit C is charged through R from the constant voltage source, V_s. The voltage, ν_c, across the (initially uncharged) capacitor voltage will rise exponentially as shown in Figure 1.92. At the same time, the current in the circuit, i, will fall, as shown in Figure 1.93.

The rate of growth of voltage with time (and decay of current with time) will be dependent upon the product of capacitance and resistance. This value is known as the time constant of the circuit. Hence:

Time constant, t = C × R

where C is the value of capacitance (F), R is the resistance (F), and t is the time constant (s).

The voltage developed across the charging capacitor, ν_c, varies with time, t, according to the relationship:

where ν_c is the capacitor voltage, V_s is the DC supply voltage, t is the time, and CR is the time constant of the circuit (equal to the product of capacitance, C, and resistance, R).

The capacitor voltage will rise to approximately 63% of the supply voltage, V_s, in a time interval equal to the time constant.

At the end of the next interval of time equal to the time constant (i.e., after an elapsed time equal to 2CR) the voltage will have risen by 63% of the remainder, and so on. In theory, the capacitor will never become fully charged. However, after a period of time equal to 5CR, the capacitor voltage will to all intents and purposes be equal to the supply voltage. At this point, the capacitor voltage will have risen to 99.3% of its final value and we can consider it to be fully charged.

During charging, the current in the capacitor, i, varies with time, t, according to the relationship:

where V_s is the DC supply voltage, t is the time, R is the series resistance and C is the value of capacitance.

The current will fall to approximately 37% of the initial current in a time equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after a total time of 2CR has elapsed) the current will have fallen by a further 37% of the remainder, and so on.

1.3.9 Waveshaping with C-R Networks

One of the most common applications of C-R networks is in waveshaping circuits. The circuits shown in Figures 1.98 and 1.100 function as simple square-to-triangle and square-to-pulse converters by, respectively, integrating and differentiating their inputs.

The effectiveness of the simple integrator circuit shown in Figure 1.98 depends on the ratio of time constant, C × R, to periodic time, t. The larger this ratio is, the more effective the circuit will be as an integrator. The effectiveness of the circuit of Figure 1.98 is illustrated by the input and output waveforms shown in Figure 1.99.

Similarly, the effectiveness of the simple differentiator circuit shown in Figure 1.100 also depends on the ratio of time constant C × R, to periodic time, t. The smaller this ratio is, the more effective the circuit will be as a differentiator.

The effectiveness of the circuit of Figure 1.100 is illustrated by the input and output waveforms shown in Figure 1.101.

1.3.10 L-R Circuits

Networks of inductors and resistors (known as L-R circuits) can also be used for timing and pulse shaping. In comparison with capacitors, however, inductors are somewhat more difficult to manufacture and are consequently more expensive.

Inductors are also prone to losses and may also require screening to minimize the effects of stray magnetic coupling. Inductors are, therefore, generally unsuited to simple timing and waveshaping applications.

Figure 1.102 shows a simple L-R network in which an inductor is connected to a constant voltage supply. When the supply is first connected, the current, i, will rise exponentially with time, as shown in Figure 1.103. At the same time, the inductor voltage V_L, will fall, as shown in Figure 1.104). The rate of change of current with time will depend upon the ratio of inductance to resistance and is known as the time constant. Hence:

Time constant, t = L/R

where L is the value of inductance (H), R is the resistance (Ω), and t is the time constant (s).

The current flowing in the inductor, i, varies with time, t, according to the relationship:

where V_s is the DC supply voltage, R is the resistance of the inductor, and L is the inductance.

The current, i, will initially be zero and will rise to approximately 63% of its maximum value (i.e., V_s/R) in a time interval equal to the time constant. At the end of the next interval of time equal to the time constant (i.e., after a total time of 2L/R has elapsed) the current will have risen by a further 63% of the remainder, and so on.

In theory, the current in the inductor will never become equal to V_s/R. However, after a period of time equal to 5L/R, the current will to all intents and purposes be equal to V_s/R. At this point, the current in the inductor will have risen to 99.3% of its final value.

The voltage developed across the inductor, ν_L, varies with time, t, according to the relationship:

where V_s is the DC supply voltage, R is the resistance of the inductor, and L is the inductance.

The inductor voltage will fall to approximately 37% of the initial voltage in a time equal to the time constant.

At the end of the next interval of time equal to the time constant (i.e., after a total time of 2L/R has elapsed) the voltage will have fallen by a further 37% of the remainder, and so on.

1.4.1 Alternating Versus Direct Current

Direct currents are currents which, even though their magnitude may vary, essentially flow only in one direction. In other words, direct currents are unidirectional. Alternating currents, on the other hand, are bidirectional and continuously reverse their direction of flow. The polarity of the e.m.f. which produces an alternating current must consequently also be changing from positive to negative, and vice versa.

Alternating currents produce alternating potential differences (voltages) in the circuits in which they flow. Furthermore, in some circuits, alternating voltages may be superimposed on direct voltage levels (see Figure 1.105). The resulting voltage may be unipolar (i.e., always positive or always negative) or bipolar (i.e., partly positive and partly negative).

1.4.2 Waveforms and Signals

A graph showing the variation of voltage or current present in a circuit is known as a waveform. There are many common types of waveform encountered in electrical circuits including sine (or sinusoidal), square, triangle, ramp or sawtooth (which may be either positive or negative going), and pulse.

Complex waveforms, like speech and music, usually comprise many components at different frequencies. Pulse waveforms are often categorized as either repetitive or nonrepetitive (the former comprises a pattern of pulses that repeats regularly while the latter comprises pulses which constitute a unique event). Some common waveforms are shown in Figure 1.106.

Signals can be conveyed using one or more of the properties of a waveform and sent using wires, cables, optical and radio links. Signals can also be processed in various ways using amplifiers, modulators, filters, etc. Signals are also classified as either analog (continuously variable) or digital (based on discrete states).

1.4.3 Frequency

The frequency of a repetitive waveform is the number of cycles of the waveform which occur in unit time. Frequency is expressed in hertz (Hz) and a frequency of 1 Hz is equivalent to one cycle per second. Hence, if a voltage has a frequency of 400 Hz, 400 cycles of it will occur in every second.

The equation for the voltage shown in Figure 1.105(A) at a time, t, is:

while that in Figure 1.105(B) is:

where ν is the instantaneous voltage, V_max is the maximum (or peak) voltage of the sine wave, V_DC, is the DC offset (where present), and f is the frequency of the sine wave.

1.4.4 Periodic Time

The periodic time (or period) of a waveform is the time taken for one complete cycle of the wave (see Figure 1.107). The relationship between periodic time and frequency is thus:

where t is the periodic time (in s) and f is the frequency (in Hz).

1.4.5 Average, Peak, Peak-Peak, and r.m.s. Values

The average value of an alternating current which swings symmetrically above and below zero will be zero when measured over a long period of time. Hence, average values of currents and voltages are invariably taken over one complete half-cycle (either positive or negative) rather than over one complete full-cycle (which would result in an average value of zero).

The amplitude (or peak value) of a waveform is a measure of the extent of its voltage or current excursion from the resting value (usually zero).

The peak-to-peak value for a wave which is symmetrical about its resting value is twice its peak value (see Figure 1.108).

The r.m.s. (or effective) value of an alternating voltage or current is the value which would produce the same heat energy in a resistor as a direct voltage or current of the same magnitude. Since the r.m.s. value of a waveform is very much dependent upon its shape, values are only meaningful when dealing with a waveform of known shape. Where the shape of a waveform is not specified, r.m.s. values are normally assumed to refer to sinusoidal conditions.

For a given waveform, a set of fixed relationships exist between average, peak, peak-peak, and r.m.s. values. The required multiplying factors are summarized for sinusoidal voltages and currents in Table 1.16.

Table 1.16 Multiplying factors for average, peak, peak-peak and r.m.s. values

1.4.6 Reactance

When alternating voltages are applied to capacitors or inductors the magnitude of the current flowing will depend upon the value of capacitance or inductance and on the frequency of the voltage. In effect, capacitors and inductors oppose the flow of current in much the same way as a resistor. The important difference being that the effective resistance (or reactance) of the component varies with frequency (unlike the case of a resistor where the magnitude of the current does not change with frequency).

1.4.7 Capacitive Reactance

The reactance of a capacitor is defined as the ratio of applied voltage to current and, like resistance, it is measured in Ohms. The reactance of a capacitor is inversely proportional to both the value of capacitance and the frequency of the applied voltage. Capacitive reactance can be found by applying the following formula:

where X_c is the reactance (in ohms), f is the frequency (in hertz), and C is the capacitance (in farads).

Capacitive reactance falls as frequency increases, as shown in Figure 1.109. The applied voltage, V_c, and current, I_c, flowing in a pure capacitive reactance will differ in phase by an angle of 90° or π/2 radians (the current leads the voltage). This relationship is illustrated in the current and voltage waveforms (drawn to a common time scale) shown in Figure 1.110 and as a phasor diagram shown in Figure 1.111.

1.4.8 Inductive Reactance

The reactance of an inductor is defined as the ratio of applied voltage to current and, like resistance, it is measured in ohms. The reactance of an inductor is directly proportional to both the value of inductance and the frequency of the applied voltage. Inductive reactance can be found by applying the formula:

where X_L is the reactance in Ω, f is the frequency in Hz, and L is the inductance in H.

Inductive reactance increases linearly with frequency as shown in Figure 1.112. The applied voltage, V_L, and current, I_L, developed across a pure inductive reactance will differ in phase by an angle of 90° or π/2 radians (the current lags the voltage). This relationship is illustrated in the current and voltage waveforms (drawn to a common time scale) shown in Figure 1.113 and as a phasor diagram shown in Figure 1.114.

1.4.9 Impedance

Figure 1.115 shows two circuits which contain both resistance and reactance. These circuits are said to exhibit impedance (a combination of resistance and reactance) which, like resistance and reactance, is measured in ohms.

The impedance of the circuits shown in Figure 1.115 is simply the ratio of supply voltage, V_S, to supply current, I_S. The impedance of the simple C-R and L-R circuits shown in Figure 1.115 can be found by using the impedance triangle shown in Figure 1.116. In either case, the impedance of the circuit is given by:

and the phase angle (between V_S and I_S) is given by:

where Z is the impedance (in ohms), X is the reactance, either capacitive or inductive (expressed in ohms), R is the resistance (in ohms), and Φ is the phase angle in radians.

1.4.10 Power Factor

The power factor in an AC circuit containing resistance and reactance is simply the ratio of true power to apparent power. Hence:

The true power in an AC circuit is the power which is actually dissipated in the resistive component. Thus:

The apparent power in an AC circuit is the power which is apparently consumed by the circuit and is the product of the supply current and supply voltage (note that this is not the same as the power which is actually dissipated as heat). Hence:

Hence:

From Figure 1.116,

Hence, the power factor of a series AC circuit can be found from the cosine of the phase angle.

1.4.11 L-C Circuits

Two forms of L-C circuits are illustrated in Figure 1.117. Figure 1.117(A) is a series resonant circuit, while Figure 1.117(B) constitutes a parallel resonant circuit. The impedance of both circuits varies in a complex manner with frequency.

The impedance of the series circuit in Figure 1.117(A) is given by:

where Z is the impedance of the circuit (in ohms), and X_L and X_C are the reactances of the inductor and capacitor respectively (both expressed in ohms).

The phase angle (between the supply voltage and current) will be +π/2 rad (i.e., +90°) when X_L > X_C (above resonance) or − π/2 rad (or −90°) when X_C > X_L (below resonance).

At a particular frequency (known as the series resonant frequency) the reactance of the capacitor, X_C, will be equal in magnitude (but of opposite sign) to that of the inductor, X_L. Due to this effective cancellation of the reactance, the impedance of the series resonant circuit will be zero at resonance. The supply current will have a maximum value at resonance (infinite in the case of a perfect series resonant circuit supplied from an ideal voltage source!).

The impedance of the parallel circuit in Figure 1.117B is given by:

where Z is the impedance of the circuit (in Ω), and X_L and X_C are the reactances of the inductor and capacitor, respectively (both expressed in Ω).

The phase angle (between the supply voltage and current) will be +π/2 rad (i.e., +90°) when X_L > X_C (above resonance) or π/2 rad (or −90°) when X_C > X_L (below resonance).

At a particular frequency (known as the parallel resonant frequency) the reactance of the capacitor, X_C, will be equal in magnitude (but of opposite sign) to that of the inductor, X_L. At resonance, the denominator in the formula for impedance becomes zero and thus the circuit has an infinite impedance at resonance. The supply current will have a minimum value at resonance (zero in the case of a perfect parallel resonant circuit).

1.4.12 L-C-R Circuits

Two forms of L-C-R network are illustrated in Figs 1.117(C) and 1.117(D); Figure 1.117(C) is series resonant while Figure 1.117(D) is parallel resonant. As in the case of their simpler L-C counterparts, the impedance of each circuit varies in a complex manner with frequency.

The impedance of the series circuit of Figure 1.117(C) is given by:

where Z is the impedance of the series circuit (in ohms), R is the resistance (in Ω), X_L is the inductive reactance (in Ω) and X_C is the capacitive reactance (also in Ω). At resonance the circuit has a minimum impedance (equal to R).

The phase angle (between the supply voltage and current) will be given by:

The impedance of the parallel circuit of Figure 1.117(D) is given by:

where Z is the impedance of the series circuit (in ohms), R is the resistance (in Ω), X_L is the inductive reactance (in Ω) and X_C is the capacitive reactance (also in Ω). At resonance the circuit has a minimum impedance (equal to R).

The phase angle (between the supply voltage and current) will be given by:

1.4.13 Resonance

The frequency at which the impedance is minimum for a series resonant circuit or maximum in the case of a parallel resonant circuit is known as the resonant frequency. The resonant frequency is given by:

where f₀ is the resonant frequency (in hertz), L is the inductance (in henries) and C is the capacitance (in farads).

Typical impedance-frequency characteristics for series and parallel tuned circuits are shown in Figs 1.118 and 1.119.

The series L-C-R tuned circuit has a minimum impedance at resonance (equal to R) and thus maximum current will flow. The circuit is consequently known as an acceptor circuit.

The parallel L-C-R tuned circuit has a maximum impedance at resonance (equal to R) and thus minimum current will flow. The circuit is consequently known as a rejector circuit.

1.4.14 Quality Factor

The quality of a resonant (or tuned) circuit is measured by its Q-factor. The higher the Q-factor, the sharper the response (narrower bandwidth), conversely the lower the Q-factor, the flatter the response (wider bandwidth), see Figure 1.120. In the case of the series tuned circuit, the Q-factor will increase as the resistance, R, decreases. In the case of the parallel tuned circuit, the Q-factor will increase as the resistance, R, increases. The response of a tuned circuit can be modified by incorporating a resistance of appropriate value either to “dampen” (low-Q) or “sharpen” (high-Q) the response. The relationship between bandwidth and Q-factor is:

where f₂ and f₁ are respectively the upper and lower cut-off (or half-power) frequencies (in Hertz), f₀ is the resonant frequency (in hertz), and Q is the Q-factor (see Figure 1.121).

1.4.15 Transformers

Transformers provide us with a means of coupling AC power or signals from one circuit to another. Voltage may be stepped-up (secondary voltage greater than primary voltage) or stepped-down (secondary voltage less than primary voltage). Since no increase in power is possible (transformers are passive components like resistors, capacitors and inductors) an increase in secondary voltage can only be achieved at the expense of a corresponding reduction in secondary current, and vice versa (in fact, the secondary power will be very slightly less than the primary power due to losses within the transformer). Typical applications for transformers include stepping-up or stepping-down mains voltages in power supplies, coupling signals in AF amplifiers to achieve impedance matching and to isolate DC potentials associated with active components.

The electrical characteristics of a transformer are determined by a number of factors including the core material and physical dimensions. The specifications for a transformer usually include the rated primary and secondary voltages and current the required power rating (i.e., the maximum power, usually expressed in volt-amperes, VA) which can be continuously delivered by the transformer under a given set of conditions, the frequency range for the component (usually stated as upper and lower working frequency limits), and the regulation of a transformer (usually expressed as a percentage of full-load). This last specification is a measure of the ability of a transformer to maintain its rated output voltage under load.

Table 1.17 summarizes the properties of three common types of transformer. Figure 1.124 shows the construction of a typical iron-cored power transformer.

Table 1.17 Characteristics of common types of transformers

1.4.16 Voltage and Turns Ratio

The principle of the transformer is illustrated in Figure 1.125. The primary and secondary windings are wound on a common low-reluctance magnetic core. The alternating flux generated by the primary winding is therefore coupled into the secondary winding (very little flux escapes due to leakage). A sinusoidal current flowing in the primary winding produces a sinusoidal flux. At any instant the flux in the transformer is given by the equation:

where Φ_max is the maximum value of flux (in webers), f is the frequency of the applied current (in hertz), and t is the time in seconds.

The r.m.s. value of the primary voltage, V_P, is given by:

Similarly, the r.m.s. value of the secondary voltage, V_S, is given by:

Now:

where N_P/N_S is the turns ratio of the transformer.

Assuming that the transformer is loss-free, primary and secondary powers (P_P and P_S, respectively) will be identical. Hence:

Hence,

Finally, it is sometimes convenient to refer to a turns-per-volt rating for a transformer. This rating is given by:

1.5.1 Types of Analysis

Various types of analysis are available within modern SPICE-based circuit simulation packages. These usually include:

Figure 1.144 shows a four-stage shift register based on J-K bistables. The result of carrying out an analysis of this circuit is shown in Figure 1.145.

Finally, Figure 1.146 shows how a simple combinational logic circuit can be rapidly “assembled” and tested and its logical function checked. This circuit arrangement shows how the exclusive-OR function can be realized using only two-input NAND gates.

1.6.1 Physical Equivalents of Electrical Components

Before we move on to the physical equivalents, let’s understand voltage, current and power. Voltage is the potential of the electron flow. Current is the amount of flow. Sometimes the best analogies are the old overused ones and that is true in this case. Think of it in terms of water in a squirt gun. Voltage is the amount of pressure in the gun. Pressure determines how far the water squirts, but a little pea shooter with a 30-foot shot and a dinky little stream won’t get you soaked. Current is the size of the water stream, but a large stream that doesn’t shoot far is not much help in a water fight. Voltage, current and power in electrical terms are related the same way. It is in fact a simple relationship; here is the equation:

(1.1)

To get power you need both voltage and current. If either one of these are zero, you get zero power output. Let’s discuss three basic components and look at how they relate to voltage and current.

1.6.2 The Resistor is Analogous to Friction

Think about what happens when you drag a heavy box across the floor. A force called friction resists the movement of the box. This friction is related to the speed of the box. The faster you try to move the box, the more the friction resists your work. It can be described by an equation.

(1.2)

Furthermore, the friction dissipates the energy loss in the system with heat. Let me rephrase that. Friction makes things get warm. Don’t believe me? Try rubbing your hands together right now. Did you feel the heat? That is caused by friction. The function of a resistor in an electrical circuit is equal to friction. The resistor resists the flow of electricity just like friction resists the speed of the box. And, guess what, it heats up as it does so. An equation called Ohm’s Law describes this relationship:

(1.3)

Do you see the similarity to the friction equation? They are exactly the same. The only real difference is the units you are working in.

1.6.3 The Inductor is Analogous to Mass

Let’s stay with the box example for now. First let’s eliminate friction, so as not to cloud our comprehension. The box is on a smooth track with virtually frictionless wheels. You notice that it takes some work to get the box going, but once moving, it coasts along nicely. In fact, it takes work to get it to stop again. How much work depends on how heavy the box is. This is known as the law of inertia. Newton postulated this long before electricity was discovered, but it applies very well to inductance. Mass resists a change in speed. Correspondingly, inductance resists a change in current.

(1.4)

(1.5)

1.6.4 The capacitor is analogous to a spring

So what does a spring do? Take hold of a spring in your mind’s eye. Stretch it out and hold it, and then let it go. What happens? It snaps back into position. A spring has a capacity to store energy. When a force is applied, it will hold that energy till it is released. Capacitance is similar to the elasticity of the spring. (One note: the spring constant that you may remember from physics texts is the inverse of the elasticity.) I always thought it was nice that the word capacitor is used to represent a component that has the capacity to store energy. (Technically an inductor can store energy too. In a capacitor the energy is stored in the electric field that is generated in and around the cap; in an inductor energy is stored in the magnetic field that is generated. This energy stored in an inductor can be tapped very efficiently at high currents. That is why most switching power supplies have an inductor in them as the primary passive component.)

(1.6)

(1.7)

1.6.5 A Tank Circuit

Take the basic tank or LC circuit. What does it do? It oscillates. A perfect circuit would go on forever at the resonant frequency. How should this appear in our mechanical circuit? Think about the equivalents: an inductor and a capacitor, a spring and mass. In a thought experiment, hook the spring up to the box from the previous drawing. Now give it a tug. What happens? It oscillates.

1.6.6 A Complex Circuit

Let’s follow this reasoning for an LCR circuit. All we need to do is add a little resistance, or friction, to the mass-spring of the tank circuit. Let’s tighten the wheels on our box a little too much so that they rub. What will happen after you give the box a tug? It will bounce back and forth a bit till it comes to a stop. The friction in the wheels slows it down. This friction component is called a damper, because it dampens the oscillation. What is it that a resistor does to an LC circuit? It dampens the oscillation.

There you have it, the world of electricity reduced to everyday items. Since these components are so similar, all the math tricks you may have learned apply as well to one system as they do to the other. Remember Fourier’s theorems? They were discovered for mechanical systems long before anyone realized that they work for electrical circuits as well. Remember all that higher math you used to know or are just now learning about—Laplace transforms, integrals, derivatives, etc.? It all works the same in both worlds. You can solve a mechanical system using Laplace methods just the same as an electrical circuit.

Back in the ’50s and ’60s, the government spent mounds of dough using electrical circuits to model physical systems as described above. Why? You can get into all sorts of integrals, derivatives and other ugly math when modeling real-world systems. All that can get jumbled quickly after a couple of orders of complexity. Think about an artillery shell fired from a tank. How do you predict where it will land? You have the friction of the air, the mass of the shell, the spring of the recoil. Instead of trying to calculate all that math by hand, you can build a circuit with all the various electrical components representing the mechanical ones, hook up an oscilloscope, and fire away. If you want to test 1000 different weights of artillery at different altitudes, electrons are much cheaper than gunpowder.

1.6.7 Learn an Intuitive Approach

1.6.8 “Lego” Engineering

1.7.1 If Only Everything Would Always Go Right…

Why are we interested in troubleshooting? Because even the best engineers take on projects whose requirements are so difficult and challenging that the circuits don’t work as expected—at least not the first time. I don’t have data on switching regulators, but I read in an industry study that when disk drives are manufactured, the fraction that fails to function when power is first applied typically ranges from 20 to 70%. Of course, this fraction may occasionally fall as low as 1% and rise as high as 100%. But, on the average, production engineers and technicians must be prepared to repair 20, 40, or 60% of these complex units. Switching-regulated power supplies can also be quite complex. If you manufacture them in batches of 100, you shouldn’t be surprised to find some batches with 12 pieces that require troubleshooting and other batches that have 46 such pieces. The troubleshooting may, as you well know, be tough with a new product whose bugs haven’t been worked out. But it can be even tougher when the design is old and the parts it now uses aren’t quite like the ones you used to be able to buy. Troubleshooting can be tougher still when there isn’t much documentation describing how the product is supposed to work, and the designer isn’t around any more. If there’s ever a time when troubleshooting isn’t needed, it’s just a temporary miracle. You might try to duck your troubleshooting for a while. You might pretend that you can avoid the issue.

And, what if you decide that troubleshooting isn’t necessary? You may find that your first batch of products has only three or four failures, so you decide that you don’t need to worry. The second batch has a 12% failure rate, and most of the rejects have the same symptoms as those of the first batch. The next three batches have failure rates of 23, 49, and 76%, respectively. When you finally find the time to study the problems, you will find that they would have been relatively easy to fix if only you had started a couple of months earlier. That’s what Murphy’s Law can do to you if you try to slough off your troubleshooting chores…we have all seen it happen.

If you have a bunch of analog circuits that you have to troubleshoot, well, why don’t you just look up the troubleshooting procedures in a book? The question is excellent, and the answer is very simple: Until now, almost nothing has been written about the troubleshooting of these circuits. The best previous write-up that I have found is a couple pages in a book by Jiri Dostal (Ref. 1.5). He gives some basic procedures for looking for trouble in a fairly straightforward little circuit: a voltage reference/regulator. As far as Dostal goes, he does quite well. But, he only offers a few pages of troubleshooting advice, and there is much to explain beyond what he has written.

Another book that has several good pages about the philosophy of troubleshooting is by John I. Smith (Ref. 1.6). Smith explains some of the foibles of wishing you had designed a circuit correctly when you find that it doesn’t work “right.” Unfortunately, it’s out of print. Analog Devices sells a Data Converter Handbook (Ref. 1.7), and it has a few pages of good ideas and suggestions on what to look for when troubleshooting data converter and analog circuits.

What’s missing, though, is general information. When I started writing about this troubleshooting stuff, I realized there was a huge vacuum in this area. So I have filled it up, and here we are.

You’ll probably use general-purpose test equipment. What equipment can you buy for troubleshooting? For now, let me observe that if you have several million dollars worth of circuits to troubleshoot, you should consider buying a $100,000 tester. Of course, for that price you only get a machine at the low end of the line. And, after you buy the machine, you have to invest a lot of time in fixturing and software before it can help you. Yes, you can buy a $90 tester that helps locate short circuits on a PC board but, in the price range between $90 and $100,000, there isn’t a lot of specialized troubleshooting equipment available. If you want an oscilloscope, you have to buy a general-purpose oscilloscope; if you want a DVM, it will be a general-purpose DVM.

Now, it’s true that some scopes and some DVMs are more suitable for troubleshooting than others (and I will discuss the differences in the next chapter), but, to a large extent, you have to depend on your wits.

Your wits: Ah, very handy to use, your wits—but, then what? One of my favorite quotes from Jiri Dostal’s book says that troubleshooting should resemble fencing more closely than it resembles wrestling. When your troubleshooting efforts seem like wrestling in the mud with an implacable opponent (or component), then you are probably not using the right approach. Do you have the right tools, and are you using them correctly? Do you know how a failed component will affect your circuit, and do you know what the most likely failure modes are? Ah, but do you know how to think about Trouble? That is this section’s main lesson.

Even things that can’t go wrong, do. One of the first things you might do is make a list of all the things that could be causing the problem. This idea can be good up to a point. I am an aficionado of stones about steam engines, and here is a story from the book Muster Builders of Steam (Ref. 1.8). A class of new 3-cylinder4-6-0 (four small pilot wheels in front of the drive wheels, six drive wheels, no little trailing wheels) steam engines had just been designed by British designer W. A. Stanier, and they were—perfect stinkers. They simply would not steam.” So the engines’ designers made a list of all the things that could go wrong and a list of all the things that could not be at fault; they set the second list aside.

The designers specified changes to be made to each new engine in hopes of solving the problem: “Teething troubles bring modifications, and each engine can carry a different set of modifications.” The manufacturing managers “shuddered as these modified drawings seemed to pour in from Derby (Ed: site of the design facility—the Drawing Office), continually upsetting progress in the works.” (Lots of fun for the manufacturing guys, eh?) In the end, the problem took a long time to find because it was on the list of “things that couldn’t go wrong.”

Allow me to quote the deliciously horrifying words from the text: “Teething troubles always present these two difficulties: that many of the clues are very subjective and that the ‘confidence trick’ applies. By the latter I mean when a certain factor is exonerated as trouble-free based on a sound premise, and everyone therefore looks elsewhere for the trouble: whereas in fact, the premise is not sound and the exonerated factor is guilty. In Stanier’s case this factor was low super-heat. So convinced was he that a low degree of super-heat was adequate that the important change to increased superheater area was delayed far longer than necessary. There were some very sound men in the Experimental Section of the Derby Loco Drawing Office at that time, but they were young and their voice was only dimly heard. Some of their quite painstaking superheater test results were disbelieved.” But, of course, nothing like that ever happened to anybody you know—right?

1.7.2 Experts Have no Monopoly on Good Advice

Another thing you can do is ask advice only of “experts.” After all, only an expert knows how to solve a difficult problem—right? Wrong! Sometimes, a major reason you can’t find your problem is because you are too close to it—you are blinded by your familiarity. You may get excellent results by simply consulting one or two of your colleagues who are not as familiar with your design: they may make a good guess at a solution to your problem. Often a technician can make a wise (or lucky) guess as easily as can a savvy engineer. When that happens, be sure to remember who saved your neck. Some people are not just “lucky”; they may have a real knack for solving tricky problems, for finding clues, and for deducing what is causing the trouble. Friends like these can be more valuable than gold.

At National Semiconductor, we usually submit a newly designed circuit layout to a review by our peers. I invite everybody to try to win a Beverage of Their Choice by catching a real mistake in my circuit. What we really call this is a “Beercheck.” It’s fun because if I give away a few pitchers of brew, I get some of my dumb mistakes corrected—mistakes that I myself might not have found until a much-later, more-painful, and more-expensive stage. Furthermore, we all get some education. And, you can never predict who will find the little picky errors or the occasional real killer mistake. All technicians and engineers are invited.

1.7.3 Learn to Recognize Clues

There are four basic questions that you or I should ask when we are brought in to do troubleshooting on someone else’s project:

As you can plainly see, the clues you get from the answers to these questions might easily solve the problem right away; if not, they may eventually get you out of the woods. So even if a failure occurs on your own project, you should ask these four questions—as explicitly as possible—of yourself or your technician or whoever was working on the project. For example, if your roommate called you to ask for a lift because the car had just quit in the middle of a freeway, you would ask whether anything else happened or if the car just died. If you’re told that the headlights seemed to be getting dimmer and dimmer, that’s a clue.

1.7.4 Ask Questions; Take Notes; Record Amount of Funny

When you ask these four questions, make sure to record the answers on paper—preferably in a notebook. As an old test manager I used to work with, Tom Milligan, used to tell his technicians, “When you are taking data, if you see something funny, Record Amount of Funny.” That was such a significant piece of advice, we called it Milligan’s Law. A few significant notes can save you hours of work. Clues are where you find them; they should be saved and savored.

Ask not only these questions but also any other questions suggested by the answers. For example, a neophyte product engineer will sometimes come to see me with a batch of ICs that have a terrible yield at some particular test. I’ll ask if the parts failed any other tests, and I’ll hear that nobody knows because the tester doesn’t continue to test a part after it detects a failure. A more experienced engineer would have already retested the devices in the RUN ALL TESTS mode, and that is exactly what I instruct the neophyte to do.

Likewise, if you are asking another person for advice, you should have all the facts laid out straight, at least in your head, so that you can be clear and not add to the confusion. I’ve worked with a few people who tell me one thing and a minute later start telling me the opposite. Nothing makes me lose my temper faster! Nobody can help you troubleshoot effectively if you aren’t sure whether the circuit is running from +12V or ±12V and you start making contradictory statements.

And, if I ask when the device started working badly, don’t tell me, “At 3:25 PM.” I’m looking for clues, such as, “About two minutes after I put it in the 125°C oven,” or, “Just after I connected the 4Ω load.” So just as we can all learn a little more about troubleshooting, we can all learn to watch for the clues that are invaluable for fault diagnosis.

1.7.5 Methodical, Logical Plans Ease Troubleshooting

Even a simple problem with a resistive divider offers an opportunity to concoct an intelligent troubleshooting plan. Suppose you had a series string of 128 1 kΩ resistors. (See Figure 1.152.) If you applied 5V to the top of the string and 0V to the bottom, you would expect the midpoint-of the string to be at 2.5V. If it weren’t 2.5V but actually 0V, you could start your troubleshooting by checking the voltage on each resistor, working down from the top, one by one. But that strategy would be absurd! Check the voltage at, say, resistor #96, the resistor which is halfway up from the midpoint to the top. Then, depending on whether that test is high, low, or reasonable, try at #112 or #80—at 5/8 or 7/8 of the span—then at #120 or #l04 or #88 or #72, branching along in a sort of binary search—that would be much more effective. With just a few trials (about seven) you could find where a resistor was broken open or shorted to ground. Such branching along would take a lot fewer than the 64 tests you would need to walk all the way down the string.

Further, if an op-amp circuit’s output were pegged, you would normally check the circuit’s op-amp, resistors, or conductors. You wouldn’t normally check the capacitors, unless you guessed that a shorted capacitor could cause the output to peg. Conversely, if the op-amp’s V_OUT was a few dozen millivolts in error, you might start checking the resistors for their tolerances. You might not check for an open-circuited or wrong-value capacitor, unless you checked the circuit’s output with a scope and discovered it oscillating!! So, in any circuit, you must study the data—your “clues”—until they lead you to the final test that reveals the true cause of your problem.

Thus, you should always first formulate a hypothesis and then invent a reasonable test or series of tests, the answers to which will help narrow down the possibilities of what is bad, and may in fact support your hypothesis. These tests should be performable. But you may define a test and then discover it is not performable or would be much too difficult to perform. Then I often think, “Well, if I could do that test, the answer would either come up ‘good’ or ‘bad.’ OK, so I can’t easily run the test. But if I assume that I’d get one or the other of the answers, what would I do next to nail down the solution? Can I skip to the next test?”

For example, if I had to probe the first layer of metal on an IC with two layers of metal (because I had neglected to bring an important node up from the first metal to the second metal), I might do several other tests instead. I would do the other tests hoping that maybe I wouldn’t have to do that probing, which is rather awkward even if I can “borrow” a laser to cut through all the layers of oxide. If I’m lucky, I may never have to go back and do that “very difficult or nearly impossible” test.

Of course, sometimes the actual result of a test is some completely unbelievable answer, nothing like the answers I expected. Then I have to reconsider—where were my assumptions wrong? Where was my thinking erroneous? Or, did I take my measurements correctly? Is my technician’s data really valid? That’s why troubleshooting is such a challenging business—almost never boring.

On the other hand, it would be foolish for you to plan everything and test nothing. Because if you did that, you would surely plan some procedures that a quick test would show are unnecessary. That’s what they call “paralysis by analysis.” All things being equal, I would expect the planning and testing to require equal time. If the tests are very complicated and expensive, then the planning should be appropriately comprehensive. If the tests are simple, as in the case of the 128 resistors in series, you could make them up as you go along. For example, the list above of resistors #80, 112, 120, 104, 88, or 72 are nominally binary choices. You don’t have to go to exactly those places—an approximate binary search would be just fine.

1.7.6 You can make Murphy’s Law Work for You

Murphy’s Law is quite likely to attack even our best designs: “If anything can go wrong, it will.” But, I can make Murphy’s Law work for me. For example, according to this interpretation of Murphy’s Law, if I drive around with a fire extinguisher, if I am prepared to put out any fire—will that make sure that I never have a fire in my car? When you first hear it, the idea sounds dumb. But, if I’m the kind of meticulous person who carries a fire extinguisher, I may also be neat and refuse to do the dumb things that permit fires to start.

Similarly, when designing a circuit I leave extra safety margins in areas where I cannot surely predict how the circuit will perform. When I design a breadboard, I often tell the technician, “Leave 20% extra space for this section because I’m not sure that it will work without modifications. And, please leave extra space around this resistor and this capacitor because I might have to change those values.” When I design an IC, I leave little pads of metal at strategic points on the chip’s surface, so that I can probe the critical nodes as easily as possible. To facilitate probing when working with 2-layer metal, I bring nodes up from the first metal through vias to the second metal. Sometimes I leave holes in my Vapox passivation to facilitate probing dice. The subject of testability has often been addressed for large digital circuits, but the underlying ideas of Design For Testability are important regardless of the type of circuit you are designing. You can avoid a lot of trouble by thinking about what can go wrong and how to keep it from going wrong before the ensuing problems lunge at you. By planning for every possibility, you can profit from your awareness of Murphy’s Law. Now, clearly, you won’t think of every possibility. (Remember, it was something that couldn’t go wrong that caused the problems with Stanier’s loco-motives.) But, a little forethought can certainly minimize the number of problems you have to deal with.

1.7.7 Consider Appointing a Czar for a Problem Area

A few years ago we had so many nagging little troubles with band-gap reference circuits at National, that I decided (unilaterally) to declare myself “Czar of Band Gaps.” The main rules were that all successful band-gap circuits should be registered with the Czar so that we could keep a log book of successful circuits; all unsuccessful circuits, their reasons for failure, and the fixes for the failures should likewise be logged in with the Czar so that we could avoid repeating old mistakes; and all new circuits should be submitted to the Czar to allow him to spot any old errors. So far, we think we’ve found and fixed over 50% of the possible errors, before the wafers were fabricated, and we’re gaining. In addition, we have added Czars for start-up circuits and for trim circuits, and a Czarina for data sheet changes, and we are considering other czardoms. It’s a bit of a game, but it’s also a serious business to use a game to try to prevent expensive errors.

I haven’t always been a good troubleshooter, but my “baptism of fire” occurred quite a few years ago. I had designed a group of modular data converters. We had to ship 525 of them, and some foolish person had bought only 535 PC (printed circuit) boards. When less than half of the units worked, I found myself in the trouble-shooting business because nobody else could imagine how to repair them. I discovered that I needed my best-triggering scope and my best DVM. I burned a lot of midnight oil. I got half-a-dozen copies each of the schematic and of the board layout. I scribbled notes on them of what the DC voltages ought to be, what the correct AC waveforms looked like, and where I could best probe the key waveforms. I made little lists of, “If this frequency is twice as fast as normal, look for Q17 to be damaged, but if the frequency is low, look for a short on bus B.”

I learned where to look for solder shorts, hairline opens, cold-soldered joints, and intermittents. I diagnosed the problems and sent each unit back for repair with a neat label of what to change. When they came back, did they work? Some did—and some still had another level or two of problems. That’s the Onion Syndrome: You peel off one layer, and you cry; you peel off another layer, and you cry some more… By the time I was done, I had fixed all but four of the units, and I had gotten myself one hell of a good education in troubleshooting.

After I found a spot of trouble, what did l do about it? First of all, I made some notes to make sure that the problem really was fixed when the offending part was changed. Then I sent the units to a good, neat technician who did precise repair work—much better than a slob like me would do. Lastly, I sent memos to the manufacturing and QC departments to make sure that the types of parts that had proven troublesome were not used again, and I confirmed the changes with ECOs (Engineering Change Orders). It is important to get the paperwork scrupulously correct, or the alligators will surely circle back to vex you again.

1.7.8 Sloppy Documentation Can End in Chapter XI

I once heard of a similar situation where an insidious problem was causing nasty reliability problems with a batch of modules. The technician had struggled to find the solution for several days. Finally, when the technician went out for lunch, the design engineer went to work on the problem. When the technician came back from lunch, the engineer told him, “I found the problem; it’s a mismatch between Q17 and R18. Write up the ECO, and when I get back from lunch I’ll sign it.” Unfortunately, the good rapport between the engineer and the technician broke down: there was some miscommunication. The technician got confused and wrote up the ECO with an incorrect version of what should be changed. When the engineer came back from lunch, he initialed the ECO without really reading it and left for a two-week vacation.

When he came back, the modules had all been “fixed,” potted, and shipped, and were starting to fail out in the field. A check of the ECO revealed the mistake—too late. The company went bankrupt. It’s a true story and a painful one. Don’t get sloppy with your paperwork; don’t let it happen to you.

1.7.9 Failure Analysis?

One of the reasons you do troubleshooting is because you may be required to do a Failure Analysis on the failure. That’s just another kind of paperwork. Writing a report is not always fun, but sometimes it helps clarify and crystallize your understanding of the problem. Maybe if a customer had forced my engineer friend to write exactly what happened and what he proposed to do about it, that disaster would not have occurred. When I have nailed down my little problem, I usually write down a scribbled quick report. One copy often goes to my boss, because he is curious why it’s been taking me so long. I usually give a copy to friends who are working on similar projects. Sometimes I hang a copy on the wall, to warn all my friends. Sometimes I send a copy to the manufacturer of a component that was involved. If you communicate properly, you can work to avoid similar problems in the future.

Then there are other things you can do in the course of your investigation. When you find a bad component, don’t just throw it in a wastebasket. Sometimes people call me and say, “Your ICs have been giving me this failure problem for quite a while.” I ask, “Can you send me some of the allegedly bad parts?’ And they reply, “Naw, we always throw them in the wastebasket…” Please don’t do that, because often the ability to troubleshoot a component depends on having several of them to study. Sometimes it’s even a case of “NTF”—“No Trouble Found.” That happens more often than not. So if you tell me, “Pease, your lousy op-amps are failing in my circuit,” and there’s actually nothing wrong with the op-amps, but it’s really a misapplication problem—I can’t help you very well if the parts all went in the trash. Please save them, at least for a while. Label them, too.

Another thing you can do with these bad parts is to open them up and see what you can see inside. Sometimes on a metal-can IC, after a few minutes with a hacksaw, it’s just as plain as day. For example, your technician says, “This op-amp failed, all by itself, and I was just sitting there, watching it, not doing anything.” But when you look inside, one of the input’s lead-bond wires has blown out, evaporated, and in the usage circuit, there are only a couple 10 kΩ resistors connected to it. Well, you can’t blow a lead bond with less than 300 mA. Something must have bumped against that input lead and shorted it to a source that could supply half an ampere. There are many cases where looking inside the part is very educational. When a capacitor fails, or a trim-pot, I get my hammer and pliers and cutters and hack-saw and look inside just to see how nicely it was (or wasn’t) built. To see if I can spot a failure mechanism—or a bad design. I’m just curious. But sometimes I learn a lot.

Now, when I have finished my inspection, and I am still mad as hell because I have wasted a lot of time being fooled by a bad component—what do I do? I usually WIDLARIZE it, and it makes me feel a lot better. How do you WIDLARIZE something? You take it over to the anvil part of the vice, and you beat on it with a hammer, until it is all crunched down to tiny little pieces, so small that you don’t even have to sweep it off the floor. It sure makes you feel better. And you know that that component will never vex you again. That’s not a joke, because sometimes if you have a bad pot or a bad capacitor, and you just set it aside, a few months later you find it slipped back into your new circuit and is wasting your time again. When you WIDLARIZE something, that is not going to happen. And the late Bob Widlar is the guy who showed me how to do it.

1.7.10 Troubleshooting by Phone—A Tough Challenge

These days, I do quite a bit of troubleshooting by telephone. When my phone rings, I never know if a customer will be asking for simple information or submitting a routine application problem, a tough problem, or an insoluble problem. Often I can give advice just off the top of my head because I know how to fix what is wrong. At other times, I have to study for a while before I call back. Sometimes, the circuit is so complicated that I tell the customer to mail or transmit the schematic to me. On rare occasions, the situation is so hard to analyze that I tell the customer to put the circuit in a box with the schematic and a list of the symptoms and ship it to me. Or, if the guy is working just a few miles up the road, I will sometimes drop in on my way home, to look at the actual problem.

Sometimes the problem is just a misapplication. Sometimes parts have been blown out and I have to guess what situation caused the overstress. Here’s an example: In June, a manufacturer of dental equipment complained of an unacceptable failure rate on LM317 regulators. After a good deal of discussion, I asked, “Where did these failures occur?” Answer: North Dakota. “When did they start to occur?” Answer: In February. I put two and two together and realized that the climate in a dentist’s office in North Dakota in February is about as dry as it can be, and is conducive to very high electrostatic potentials. The LM317 is normally safe against electrostatic discharges as high as 3 or 4 kV, but walking across a carpeted floor in North Dakota in February can generate much higher voltages than that. To make matters worse, the speed-control rheostat for this dental instrument was right out in the handle. The wiper and one end of the rheostat were wired directly to the LM317’s ADJUST pin; the other end of the rheostat was connected to ground by way of a 1 kΩ resistor located back in the main assembly (see Figure 1.153). The speed-control rheostat was just wired up to a ct as a lightning rod that conducted the ESD energy right into the ADJUST pin.

The problem was easily solved by rewiring the resistor in series with the IC’s ADJUST pin. By swapping the wires and connecting the rheostat wiper to ground (see Figure 1.154), much less current would take the path to the ADJUST pin and the diffused resistors on the chip would not be damaged or zapped by the current surges. Of course, adding a small capacitor from the ADJ pin to ground would have done just as well, but some customers find it easier to justify moving a component than adding one…

A similar situation occurs when you get a complaint from Boston in June, “Your op-amps don’t meet spec for bias current.” The solution is surprisingly simple: Usually a good scrub with soap and water works better than any other solvent to clean off the residual contaminants that cause leakage under humid conditions. (Fingerprints, for example…)

1.7.11 When Computers Replace Troubleshooters, Look Out

Now, let’s think—what needs troubleshooting? Circuits? Television receivers? Cars? People? Surely doctors have a lot of troubleshooting to—they listen to symptoms and try to figure out the solution. What is the natural temptation? To let a computer do all the work! After all, a computer is quite good at listening to complaints and symptoms, asking wise questions, and proposing a wise diagnosis. Such a computer system is sometimes called an Expert System—part of the general field of Artificial Intelligence. But, I am still in favor of genuine intelligence. Conversely, people who rely on Artificial Intelligence are able to solve some kinds of problems, but you can never be sure if they can accommodate every kind of Genuine Stupidity as well as Artificial Stupidity. (That is the kind that is made up especially to prove that Artificial Intelligence works just great.)

I won’t argue that the computer isn’t a natural for this job; it will probably be cost-effective, and it won’t be absent-minded. But, I am definitely nervous because if computers do all the routine work, soon there will be nobody left to do the thinking when the computer gives up and admits it is stumped. I sure hope we don’t let the computers leave the smart troubleshooting people without jobs, whether the object is circuits or people.

My concern is shared by Dr. Nicholas Lembo, the author of a study on how physicians make diagnoses, which was published in the New England Journal of Medicine. He recently told the Los Angeles Times, “With the advent of all the new technology, physicians aren’t all that much interested (in bedside medicine) because they can order a $300 to $400 test to tell them something they could have found by listening.” An editorial accompanying the study commented sadly: “The present trend…may soon leave us with a whole new generation of young physicians who have no confidence in their own ability to make worthwhile bedside diagnoses.” Troubleshooting is still an art, and it is important to encourage those artists.

1.7.12 The Computer Is Your Helper … and Friend …???

I read in the San Francisco Examiner (Ref. 1.9) about a case when SAS, the Scandinavian airline, implemented an “Expert System” for its mechanics:

“Management knew something was wrong when the quality of the work started decreasing. It found the system was so highly mechanized that mechanics never questioned its judgment. So the mechanics got involved in its redesign. They made more decisions on the shop floor and used the computer to augment those decisions, increasing productivity and cutting down on errors. ‘A computer can never take over everything,’ said one mechanic. ‘Now there are greater demands on my judgment, (my job) is more interesting.’” What can I add? Just be thoughtful. Be careful about letting the computers take over.

1.7.13 No Problems?? No Problem … Just Wait …

Now, let’s skip ahead and presume we have all the necessary tools and the right receptive attitude. What else do we need? What is the last missing ingredient? That reminds me of the little girl in Sunday School who was asked what you have to do to obtain forgiveness of sin. She shyly replied, “First you have to sin.” So, to do troubleshooting, first you have to have some trouble. But, that’s usually not a problem; just wait a few hours, and you’ll have plenty. Murphy’s Law implies that if you are not prepared for trouble, you will get a lot of it. Conversely, if you have done all your homework, you may avoid most of the possible trouble.

I’ve tried to give you some insights on the philosophy of how to troubleshoot. Don’t believe that you can get help on a given problem from only one specific person. In any particular case, you can’t predict who might provide the solution. Conversely, when your buddy is in trouble and needs help, give it a try—you could turn out to be a hero. And, even if you don’t guess correctly, when you do find out what the solution is, you’ll have added another tool to your bag of tricks.

When you have problems, try to think about the right plan to attack and nail down the problem. So, if you do your “philosophy homework,” it may make life easier and better for you. You’ll be able not only to solve problems, but maybe even to avoid problems. That sounds like a good idea to me!

1.7.14 Choosing the Right Equipment

As discussed earlier, the most important thing you need for effective troubleshooting is your wits. In addition to those, however, you’ll normally want to have some equipment. This section itemizes the equipment that is necessary for most general troubleshooting tasks; some you can buy off the shelf, and some you can build yourself.

Before you begin your troubleshooting task, you should know that the equipment you use has a direct bearing on the time and effort you must spend to get the job done. Also know that the equipment you need to do a good job depends on the kind of circuit or product you are working on. For example, a DVM may be unnecessary for troubleshooting some problems in digital logic. And, the availability and accessibility of equipment may present certain obstacles. If you only have a mediocre oscilloscope and your company can’t go out and buy or rent or borrow a fancy full-featured scope, then you will have to make do.

If you lack a piece of equipment, be aware that you are going into battle with inadequate tools; certain clues may take you much longer than necessary to spot. In many cases when you spent too much time finding one small problem, the time was wasted simply because you were foolish or were unaware of a particular troubleshooting technique; but, in other cases, the time was wasted because of the lack of a particular piece of equipment. It’s important for you to recognize this last-mentioned situation. Learning when you’re wasting time because you lack the proper equipment is part of your education as a troubleshooter.

In addition to the proper tools, you also need to have a full understanding of how both your circuit and your equipment are supposed to work. I’m sure you’ve seen engineers or technicians work for many fruitless hours on a problem and then, when they finally find the solution, say, “Oh, I didn’t know it was supposed to work that way.” You can avoid this scenario by using equipment that you are comfortable and familiar with.

The following equipment is essential for most analog-circuit troubleshooting tasks. This list can serve as a guide to both those setting up a lab and those who just want to make sure that they have everything they need—that they aren’t missing any tricks.

A short-circuit-detector circuit. This tool comes in handy when you have to repair a lot of large PC boards: It can help you find a short circuit between the ground bus and the power or signal busses. It’s true that a sensitive DVM can also perform this function, but a short-circuit detector is much faster and more efficient. Also, this circuit turns itself off and draws no current when the probe is not connected. In the short-circuit-detector circuit shown in Figure 1.163, the LM10 op-amp amplifies the voltage drop and feeds it to the LM331 voltage-to-frequency converter, which you set up to emit its highest pitch when V_in = 0 mV. When using this circuit, use a 50- to 100-mA current-limited power supply. To calibrate the circuit, first ground the detector’s two probes and trim the OFFSET ADJUST for a high pitch. Then, move the positive test probe to V_s at A and trim the GAIN ADJUST for a low pitch. Figure 1.163 illustrates a case in which one of the five major power supply busses of the circuit-in-trouble has a solder short to ground.

To find the exact location of the short, you simply slide the positive input probe along the busses. In this example, if you slide it from A toward B or D, the pitch won’t change because there is no change in voltage at these points—no current flowing along those busses. But, if you slide the probe along the path from A to C or from K to M, the pitch will change because the voltage drop is changing along those paths. It’s an easy and natural technique to learn to follow the shifting frequency signals.

An AM radio. What do you do when trouble is everywhere? A typical scenario starts out like this: You make a minor improvement on a linear circuit, and when you fire it up you notice a terrible oscillation riding on the circuit’s output. You check everything about the circuit, but the oscillation remains. In fact, the oscillation is riding on the output, the inputs, on several internal nodes. and even on ground. You turn off the DVM, the function generator, the soldering iron, and finally even the power supplies, but the oscillation is still there.

Now you start looking around the lab to see who has started a new oscillator or switching regulator that is doubling as a medium-power transmitter. Aside from yelling, “Who has a new circuit oscillating at 87 kHz?” what can you do to solve the problem? One useful tool is an ordinary AM transistor radio. As we have all learned, FM radios reject many kinds of noise, but AM radios scoop up noise at repetition rates and frequencies that would surprise you.

How can a crummy little receiver with an audio bandwidth of perhaps 5 kHz detect noise in the kilohertz and megahertz regions? Of course, the answer is that many repetitive noise-pulse trains (whose repetition rates are higher than the audible spectrum but below the AM frequency band) have harmonics that extend into the vicinity of 600 kHz, where the AM receiver is quite sensitive. This sensitivity extends to signals with amplitudes of just a few microvolts per meter.

If you are skeptical about an AM radio’s ability to detect these signals, tune its dial down to the low end, between stations. Then, hold it near a DVM or a computer or computer keyboard, and listen for the hash. Notice, too, that the ferrite stick antenna has definite directional sensitivity, so you can estimate where the noise is coming from by using either the null mode or pointing the antenna to get the strongest signal. So, the humble AM radio may be able to help you as you hike around the lab and smile pleasantly at your comrades until you find the culprit whose new switching regulator isn’t working quite right but which he neglected to turn off when he went out to get a cup of coffee.

The grid-dip meter. On other occasions, the frequency and repetition rate of the noise are so high that an AM receiver won’t be helpful in detecting the problem. What’s the tool to use then? Back in the early days of radio, engineers found that if you ran a vacuum-tube oscillator and immersed it in a field of high-power oscillations at a comparable frequency, the tube’s grid current would shift or dip when the frequencies matched. This tool became known as the “grid-dip meter.” I can’t say that I am an expert in the theory or usage of the grid-dip meter, but I do recall being impressed in the early days of monolithic ICs: A particular linear circuit was oscillating at 98 MHz, and the grid-dip meter could tickle the apparent rectified output error as I tuned the frequency dial back and forth.

That was 25 years ago, and, of course, Heathkit² has discontinued their old Grid Dip and Tunnel Dip meters in favor of a more modern design. The new one, simply dubbed HD-1250 “Dip Meter,” uses transistors and tetrode FETs. At the bargain price of $89, every lab should have one. They’ll help you ferret out the source of nasty oscillations as high as 250 MHz. The literature that comes with the HD-1250 dip-meter kit also lists several troubleshooting tips.

When grid-dip meters first became popular, the fastest oscilloscope you could buy had a bandwidth of only a few dozen megahertz. These days, it is possible to buy a scope with a bandwidth of many hundreds of megahertz, so there are fewer occasions when you might need a grid-dip meter. Still, there are times when it is exactly the right tool. For example, you can use its oscillator to activate passive tuned circuits and detect their modes of resonance. Also, in a small company where you can’t afford to shell out the many thousands of dollars for a fast scope, the dip meter is an inexpensive alternative.

You’ve come to the end of my list of essential equipment for ordinary analog circuit troubleshooting. Depending on your circuit, you may not need all these items; and, of course, the list did not include a multitude of other equipment that you may find useful. Logic analyzers, impedance analyzers, spectrum analyzers, programmable current pumps, capacitance meters and testers, and pulse generators can all ease various troubleshooting tasks.