Amplifiers and signal generators

Amplifiers make weak signals stronger, and oscillators create signals from DC power. Together they appear in every radio, audio system, sensor interface and communication link. This topic covers gain and its measurement in decibels, types of amplifiers, design of small-signal BJT/MOSFET amplifiers, negative feedback, power amplifier classes, and the principles of sinusoidal oscillators and waveform generators. NEC MCQs often ask about efficiency of amplifier classes, the Barkhausen criterion, oscillator frequency formulas and effects of negative feedback.

Key concepts

Amplification and gain

• Gain = output/input. Voltage gain $A_v = V_o/V_i$, current gain $A_i = I_o/I_i$, power gain $A_p = A_vA_i$.
• In decibels: $A_{dB} = 20\log_{10}A_v$ (voltage/current) or $10\log_{10}A_p$ (power). Gains in dB add for cascaded stages.
• Bandwidth: range between lower and upper −3 dB (half-power) frequencies.

Amplifier types

• Voltage amplifier: high input resistance, low output resistance (ideal $R_i = \infty$, $R_o = 0$).
• Current amplifier: low $R_i$, high $R_o$.
• Transconductance (output current per input volt) and transresistance (output volt per input current) amplifiers.
• By application: audio, RF/tuned, video, DC, power amplifiers.

Low-frequency small-signal amplifier design

1. Biasing: choose Q-point in middle of active (BJT) or saturation (MOSFET) region, usually by voltage-divider bias with emitter/source resistor.
2. Small-signal parameters: BJT $g_m = I_C/V_T$, $r_\pi = \beta/g_m$; MOSFET $g_m = 2I_D/V_{ov}$.
3. Gain and impedance:
   • CE: $A_v \approx -g_mR_C$ (with $R_E$ unbypassed: $A_v \approx -R_C/R_E$); $R_i = R_1\|R_2\|r_\pi$; $R_o \approx R_C$.
   • CS: $A_v = -g_mR_D$; $R_i = R_1\|R_2$ (very high).
4. Coupling capacitors set the low cut-off frequency; bypass capacitor across $R_E$ raises gain.

Negative feedback (part of output fed back out of phase)

• Closed-loop gain $A_f = A/(1 + A\beta)$.
• Effects: reduces and stabilises gain, increases bandwidth (gain-bandwidth product constant), reduces distortion and noise, changes impedances.
• Topologies: voltage-series (raises $R_i$, lowers $R_o$), voltage-shunt, current-series, current-shunt (lowers $R_i$, raises $R_o$).

Power amplifiers

Class	Conduction angle	Max efficiency	Notes
A	360°	25% (resistive load), 50% (transformer coupled)	lowest distortion
B (push-pull)	180°	78.5% ($\pi/4$)	crossover distortion
AB	180°–360°	between A and B (~50–78%)	small bias removes crossover distortion
C	< 180°	> 78.5% (up to ~90%)	tuned RF amplifiers only

Oscillators

• An oscillator is an amplifier with positive feedback and no external input.
• Barkhausen criterion: loop gain $|A\beta| = 1$ and total phase shift around the loop = 0° or 360°. In practice $|A\beta|$ is made slightly >1 to start oscillation from noise.
• RC oscillators (audio range):
  • RC phase-shift: three RC sections give 180°, amplifier gives 180°; $f = \frac{1}{2\pi RC\sqrt6}$; BJT/op-amp gain needed ≥ 29.
  • Wien bridge: $f = \frac{1}{2\pi RC}$; feedback factor 1/3 so gain ≥ 3; non-inverting amplifier.
• LC oscillators (RF): Hartley (tapped inductor, $L = L_1 + L_2 + 2M$), Colpitts (tapped capacitor, $C = C_1C_2/(C_1+C_2)$), Clapp (Colpitts with extra series C for stability). $f = 1/(2\pi\sqrt{LC})$.
• Crystal oscillator: quartz crystal uses the piezoelectric effect; very high Q (10⁴–10⁶) → excellent frequency stability. Has series and parallel resonant frequencies very close together.

Waveform generators

• Square wave: astable multivibrator (op-amp with RC and positive feedback Schmitt trigger, or 555 timer). Op-amp astable period $T = 2RC\ln\frac{1+\beta}{1-\beta}$.
• Triangular wave: integrate a square wave (Schmitt trigger + integrator loop).
• Sawtooth wave: integrator/ramp charged by constant current and quickly reset (e.g. UJT relaxation oscillator, or unequal charge/discharge times).

High-yield points

• Barkhausen criterion: $|A\beta| = 1$ and loop phase shift 0° or 360°.
• Maximum efficiency: class A 25% (50% transformer-coupled), class B 78.5%, class C above 78.5%.
• RC phase-shift: $f = 1/(2\pi RC\sqrt6)$, gain ≥ 29; Wien bridge: $f = 1/(2\pi RC)$, gain ≥ 3.
• Negative feedback: $A_f = A/(1 + A\beta)$, bandwidth × $(1 + A\beta)$, gain-bandwidth product constant.
• Hartley uses a tapped inductor, Colpitts a tapped capacitor; crystal oscillators give the best frequency stability.

Formulas

$A_f = \frac{A}{1+A\beta},\qquad BW_f = BW(1+A\beta)$

$\eta = \frac{P_{ac,out}}{P_{dc,in}}\times100\%$

Worked example

An amplifier with open-loop gain A = 1000 and bandwidth 20 kHz has negative feedback with β = 0.009. Find closed-loop gain and new bandwidth.

1. $A\beta = 1000\times0.009 = 9$; $1 + A\beta = 10$.
2. $A_f = 1000/10 = 100$ (40 dB).
3. $BW_f = 20\text{ kHz}\times10 = 200$ kHz. Gain-bandwidth product stays $2\times10^7$ Hz. ✓

Exam tips

• Class B maximum efficiency = 78.5%; Class A (resistive) = 25%.
• RC phase-shift oscillator needs gain ≥ 29; Wien bridge needs gain ≥ 3.
• Crystal oscillators are chosen for frequency stability, not power.
• Negative feedback reduces gain but improves everything else (bandwidth, stability, distortion).
• Hartley = tapped L; Colpitts = tapped C (remember "C for Colpitts, C for capacitor").

Exam-style questions

From Calmon's question bank, which has 25 questions on this topic.

1. An amplifier delivers 1 W of output power for an input power of 1 mW. What is its power gain in decibels?

• A. 1000 dB
• B. 60 dB
• C. 3 dB
• D. 30 dB

Answer: D. $G = 10\log_{10}(P_o/P_i) = 10\log_{10}(1000) = 30$ dB.

2. What is the maximum theoretical efficiency of a Class B push-pull power amplifier?

• A. 25 %
• B. 100 %
• C. 78.5 %
• D. 50 %

Answer: C. For Class B, $\eta_{max} = \pi/4 \approx 78.5\%$. A Class A amplifier with a resistive load reaches only 25 %, or 50 % with a transformer-coupled load.

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