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Signals may be analogue (continuous in time and amplitude) or digital (discrete). A periodic signal is characterised by amplitude, frequency f, period T = 1/f and phase. Mean value and RMS value (the square root of the mean of the square) measure size; RMS gives the equivalent DC power. Any periodic signal is a sum of sinusoids (Fourier series), so a circuit's frequency response predicts what it does to any signal. Amplifiers are described by gain (often in decibels: 20 log10 of the voltage ratio) and bandwidth.

Kirchhoff's laws and Ohm's law apply to any circuit; for linear circuits Thevenin and Norton equivalents and superposition simplify the analysis. Impedance and phasors handle sinusoidal steady state; the RC circuit acts as a low-pass or high-pass filter depending on where the output is taken. Electronic devices are usually non-linear, so linear methods are applied to small signals around an operating point.

1. What is the RMS value of a sinusoid with amplitude Vm? 2. Express a voltage gain of 100 in decibels. 3. Why can linear methods be applied to non-linear devices?

1. Vm/sqrt(2). 2. 40 dB. 3. For small signals around an operating point the device behaves approximately linearly.

A non-linear element has a current-voltage characteristic that is not a straight line. Graphical solution: the load line of the linear part of the circuit intersects the device characteristic at the operating (bias) point. Numerical or piecewise-linear models replace the curve by straight segments, choosing the segment by assuming a state and checking the assumption.

A diode is a pn junction. Forward bias (positive voltage on the p side): current rises exponentially above a threshold of about 0.6-0.7 V for silicon (Shockley equation I = Is (exp(V/(n VT)) - 1), with thermal voltage VT about 25 mV at room temperature). Reverse bias: only a tiny leakage current until breakdown. Models: ideal diode (short circuit forward, open reverse), constant-voltage-drop model (0.7 V when conducting), and piecewise-linear model with a forward resistance.

Half-wave rectifier: one diode passes only positive half cycles. Full-wave rectifier: a centre-tapped transformer with two diodes, or a bridge of four diodes, uses both half cycles. A smoothing capacitor charges to the peak and discharges through the load; ripple is smaller for a larger capacitor or a higher load resistance. Zener diode: operated in reverse breakdown, where the voltage stays nearly constant (Zener voltage), used as a simple voltage regulator with a series resistor. Also LEDs and photodiodes are diodes for light emission and detection.

1. What is the forward threshold voltage of a silicon diode? 2. Explain how a bridge rectifier works. 3. What determines ripple in a filtered rectifier? 4. How is a Zener regulator connected?

1. About 0.6-0.7 V. 2. Four diodes route both half cycles of the input so the load current always has the same direction. 3. The filter capacitance, the load current and the frequency. 4. Reverse-biased across the load, in parallel with it, with a series resistor from the supply.

The BJT has three regions: emitter, base and collector (npn or pnp). In the forward-active region the base-emitter junction is forward biased (V_BE about 0.7 V) and the base-collector junction reverse biased; then I_C = beta I_B with current gain beta typically 100-300, and I_E = I_B + I_C. Saturation (both junctions forward biased): the transistor is a closed switch with V_CE(sat) about 0.2 V. Cut-off (base-emitter not forward biased): open switch. Biasing sets the operating point with resistors: a voltage divider at the base and an emitter resistor stabilise it against variations of beta. Amplifier configurations: common emitter (voltage gain, phase inversion), common collector (emitter follower, unity gain and low output resistance) and common base.

The MOSFET has gate, drain, source (and body). For an n-channel enhancement device, when V_GS exceeds the threshold V_T a channel forms. Regions: cut-off (V_GS below V_T), triode or ohmic (V_DS small, behaves like a voltage-controlled resistor) and saturation (V_DS above V_GS minus V_T; I_D = (k/2)(V_GS - V_T) squared, used for amplification). The gate is insulated, so the input resistance is very high. Uses: digital switch (basis of CMOS logic), low-power amplifiers and power switching. Compared with BJTs: voltage controlled, high input impedance, lower power consumption, and easy to integrate.

1. Give the relation between collector and base current in the active region. 2. What are the three operating regions of a BJT? 3. When does an n-channel MOSFET conduct? 4. Name an advantage of MOSFETs over BJTs.

1. I_C = beta I_B. 2. Cut-off, active and saturation. 3. When V_GS exceeds the threshold voltage V_T. 4. Very high input resistance and low power consumption, and easy integration.