Single-stage amplifiers

A transistor has three terminals, and an amplifier stage uses one of them for the input, one for the output and the third as common to both, connected to signal ground. That gives three basic configurations for each type of transistor: common emitter, common base and common collector for the BJT, and common source, common gate and common drain for the MOSFET. Each has a characteristic voltage gain, input resistance and output resistance, and real amplifiers combine them, choosing each stage for the job it does best. This lesson analyzes all six with the small-signal models of lesson 10 and finishes the first stage of the pedestrian signal's microphone amplifier.

Amara's specification for that amplifier is a mid-band voltage gain of about 100 from the microphone to the envelope detector, an input resistance of at least 10 kΩ so the 2 kΩ microphone is not loaded heavily, an output that can drive the detector's 1 µF capacitor through a diode, and low enough distortion that the noise-level reading is not biased by the amplifier itself. One stage cannot meet all of that; two can.

The common-emitter amplifier

In the common-emitter (CE) amplifier, the signal enters at the base, the output is taken from the collector, and the emitter is at signal ground, either connected directly or through a bypass capacitor across R_E. The DC bias is the voltage-divider circuit of lesson 7; coupling capacitors pass the signal in and out while blocking DC. With the emitter bypassed, the small-signal analysis of lesson 10 gives

where R_B = R_1 ∥ R_2. The CE stage has high voltage gain, often a hundred or more, inverts the signal, and has moderate input and output resistances. Its weaknesses are the ones lesson 10 exposed: the gain depends on g_m, so on the bias current and temperature, and with the whole input signal across the base–emitter junction it distorts at a few millivolts.

Emitter degeneration

Leaving part of the emitter resistance, R_E1, unbypassed changes the stage completely. Using the T model, the signal current in the emitter is v_b/(r_e + R_E1), and almost all of it flows in the collector, so

(neglecting r_o). When R_E1 is much larger than r_e, the gain is set by a ratio of two resistors and no longer depends on the transistor: emitter degeneration is negative feedback, and like all negative feedback it trades gain for stability, linearity and bandwidth. The input resistance rises by the factor (β + 1), because the emitter resistor appears multiplied by β + 1 when seen from the base, a rule called resistance reflection. The signal across the base–emitter junction is only a fraction r_e/(r_e + R_E1) of the input, so the stage can handle signals tens of times larger before distorting.

The common-base amplifier

In the common-base (CB) amplifier, the signal enters at the emitter, the output is taken from the collector, and the base is at signal ground. The collector current still follows the emitter current, so the voltage gain is about +g_m R_C, as large as the CE stage's and not inverted, but the input resistance looking into the emitter is only r_e, tens of ohms. The CB stage is therefore a current buffer: it accepts a current at a low impedance and delivers almost the same current at the high-impedance collector. It shines at high frequencies, because it avoids the Miller effect described in lesson 12, and in the cascode, a CE stage stacked under a CB stage, which combines high gain with wide bandwidth.

The common-collector amplifier: the emitter follower

In the common-collector (CC) amplifier, better known as the emitter follower, the signal enters at the base, the output is taken from the emitter, and the collector goes straight to the supply, which is signal ground. The emitter follows the base, one V_BE lower, so the voltage gain is just under 1. What the stage provides is impedance transformation: its input resistance is the load reflected up by β + 1, and its output resistance is the source resistance divided by β + 1, plus r_e:

Here R_L' = R_E ∥ R_L. An emitter follower lets a high-resistance source drive a low-resistance load with almost no loss: it is a voltage buffer. It is the output stage of the Zener-plus-transistor regulator of lesson 4, the output stage of many op amps and audio amplifiers, and the natural last stage of Amara's microphone amplifier, where it will drive the envelope detector.

The MOSFET configurations

The three MOSFET stages behave like their BJT counterparts, with two differences: the gate draws no current, so input resistances are set entirely by the bias network, and g_m is smaller at a given current. The common-source (CS) amplifier gives A_vo = −g_m(R_D ∥ r_o), or about −R_D/(1/g_m + R_S1) with an unbypassed source resistor, and an input resistance equal to the gate divider, which can be megohms. The common-gate (CG) stage has an input resistance of about 1/g_m and a non-inverting gain g_m R_D. The common-drain stage, the source follower, has a gain somewhat below 1, about g_m R_L'/(1 + g_m R_L'), and an output resistance of about 1/g_m, larger than an emitter follower's because g_m is smaller.

# Mid-band comparison of BJT stages at the same bias (IC = 1 mA, beta = 150, VA = 100 V)
VT, IC, beta, VA = 0.025, 1e-3, 150, 100.0
gm, re = IC / VT, VT / IC * beta / (beta + 1)
rpi, ro = beta / gm, VA / IC
RB, RC, RE1, RE, Rsig, RL = 15e3, 5.1e3, 100.0, 2.2e3, 2e3, 10e3
par = lambda *r: 1 / sum(1 / x for x in r)
stages = {
    "CE bypassed":   (-gm * par(RC, ro), par(RB, rpi), par(RC, ro)),
    "CE, RE1=100":   (-beta / (beta + 1) * RC / (re + RE1), par(RB, (beta + 1) * (re + RE1)), RC),
    "CB":            (gm * RC, re, RC),
    "CC follower":   (par(RE, RL) / (par(RE, RL) + re), par(RB, (beta + 1) * (re + par(RE, RL))),
                      par(RE, re + par(Rsig, RB) / (beta + 1))),
}
print(f"{'stage':14s} {'Avo':>8s} {'Rin':>10s} {'Rout':>10s} {'gain from 2k source into 10k load':>36s}")
for name, (a, rin, rout) in stages.items():
    overall = rin / (rin + Rsig) * a * RL / (RL + rout)
    print(f"{name:14s} {a:8.1f} {rin:9.0f}  {rout:9.0f}  {overall:24.1f}")

stage               Avo        Rin       Rout    gain from 2k source into 10k load
CE bypassed      -194.1      3000       4853                     -78.4
CE, RE1=100       -40.6      8353       5100                     -21.7
CB                204.0        25       5100                       1.7
CC follower         1.0     14227         36                       0.9

Signal swing and choosing the Q-point

An amplifier's output can swing only so far. In a CE stage the collector can rise toward V_CC as the transistor approaches cutoff, and it can fall only until the transistor saturates, about V_E + 0.3 V. For the largest symmetrical swing, the collector should sit roughly midway between those limits, taking into account that with a load connected, the signal sees R_C ∥ R_L, so the downward swing is also limited by the current available: the collector can drop by at most about I_C(R_C ∥ R_L). Daniel's rule for new designers is to calculate the swing limits in both directions and confirm that the largest expected signal fits inside both with margin.

Completing the microphone amplifier

Putting the pieces together gives Cedarline's microphone amplifier: two degenerated CE stages for gain, each giving about −10 to −15 with good linearity, followed by an emitter follower to drive the envelope detector. Two inverting stages give a non-inverted output, the gains multiply to roughly 100 to 200 after loading, and each stage's gain is set by resistor ratios rather than by β or temperature. In ELE-340 the same job would be done more elegantly with negative feedback around a multi-stage amplifier or with an op amp, but the discrete version teaches what goes on inside one.