Analog Electronics Solved Problems with Worked Examples

Analog electronics deals with continuously varying signals and the devices that process them: diodes, bipolar and field effect transistors, and operational amplifiers. It covers amplification, filtering, rectification and signal conditioning, and it remains essential because sensors and the physical world are analog.

This page works four of the standard problems through in full with numbers: the Q-point of a voltage-divider-biased stage, small-signal gain with and without the bypass capacitor, inverting and non-inverting op-amp gain, and RC filter cutoff. Each shows the method rather than only the answer.

Transistor biasing and Q-point calculation, small-signal gain, op-amp configurations and their limitations, diode rectifier circuits, filter cutoff and roll-off, and feedback with its effect on gain, bandwidth and stability. Numerical questions concentrate heavily on biasing and on gain calculations, while viva questions tend to probe the assumptions behind each formula.

Analog circuits handle signals that vary continuously over a range, so amplitude carries information and noise adds directly to it. Digital circuits use discrete levels, which gives noise immunity and easy storage, but every digital system still needs analog circuitry at its interface.

Roughly 0.7 V for a silicon diode and about 0.3 V for germanium, once conducting. For many circuits this constant-drop model is accurate enough; the exponential model is needed only where the precise current-voltage relationship matters, such as in temperature-sensitive or logarithmic circuits.

Half-wave rectification passes only one half of each input cycle, so ripple is at the supply frequency. Full-wave rectification uses both halves, doubling the ripple frequency and making smoothing easier, which is why full-wave bridges are standard in power supplies.

Because the emitter resistor provides negative feedback that holds the operating point steady: a rise in collector current raises the emitter voltage, reducing the base-emitter voltage and opposing the change. The Q-point then depends on resistor ratios rather than on the transistor's beta.

Because beta varies widely between nominally identical devices and changes with temperature and collector current. A bias design whose operating point depends on beta will drift and will not reproduce across a production batch, so good designs deliberately make the Q-point independent of it.

Find the base voltage from the divider, subtract the base-emitter drop to get the emitter voltage, divide by the emitter resistor for the emitter current, take collector current as approximately equal, then compute the collector voltage and subtract the emitter voltage for the collector-emitter voltage.

It is the intrinsic emitter resistance seen by small signals, approximately the thermal voltage of about 26 mV at room temperature divided by the emitter current. Because it depends on operating current, any gain figure derived from it must state the bias point used.

Because the capacitor shorts the emitter resistor at signal frequencies, removing the negative feedback that it provides to AC signals while leaving it in place for DC bias. Gain rises substantially, but it becomes dependent on the operating point rather than on a resistor ratio.

Infinite open-loop gain, infinite input impedance, zero output impedance, infinite bandwidth and zero offset. With negative feedback these lead to two working rules: no current enters the inputs, and the two inputs sit at the same voltage, known as the virtual short.

The negative ratio of the feedback resistor to the input resistor. The minus sign indicates inversion, a 180 degree phase shift, and omitting it is a common error. Unlike the non-inverting configuration, this arrangement can provide gains of less than one.

It is the roughly constant product of closed-loop gain and bandwidth for an op-amp. With a one megahertz product, a gain of one hundred leaves about ten kilohertz of bandwidth. A requirement for both high gain and wide bandwidth usually means splitting the design across two stages.

Slew rate is the maximum rate at which an op-amp output can change, usually quoted in volts per microsecond. It limits large-signal performance independently of bandwidth, so a circuit can have adequate small-signal bandwidth yet still distort a fast, large-amplitude waveform.

Cutoff equals one divided by two pi times resistance times capacitance. At that frequency the output is three decibels below the passband, about seventy per cent of the input amplitude, with forty-five degrees of phase shift and a twenty decibel per decade roll-off beyond it.

It stabilises gain against device variation, reduces distortion, extends bandwidth and allows input and output impedances to be set by design, all at the cost of gain. The risk is instability: if feedback becomes positive while loop gain is at least unity, the circuit oscillates.