Analog and Digital Electronics

Syllabus

Simple diode circuits (clipping, clamping, rectifiers); amplifiers (biasing, equivalent circuit, frequency response); oscillators and feedback amplifiers; operational amplifiers and their applications; active filters (Sallen-Key, Butterworth); VCOs and timers; combinational and sequential logic circuits; multiplexers, demultiplexers; Schmitt triggers; sample and hold circuits; A/D and D/A converters.

Key concepts and formulas

Rectifiers (peak V_m, ideal diodes):

A capacitor filter on a full-wave rectifier gives a peak-to-peak ripple of about V_m/(2fRC).

Transistors. I_C = βI_B, I_E = (β + 1)I_B, α = β/(β + 1). Small-signal transconductance g_m = I_C/V_T (V_T ≈ 25 mV at room temperature), r_π = β/g_m. Common-emitter voltage gain ≈ −g_mR_C. Voltage-divider bias gives a stable operating point.

Feedback and oscillators. Negative feedback: A_f = A/(1 + Aβ), which stabilises gain and widens bandwidth by (1 + Aβ). Barkhausen criterion for oscillation: |Aβ| = 1 with total phase shift 0° (or 360°). RC phase shift oscillator: A ≥ 29; Wien bridge oscillator f = 1/(2πRC) with A ≥ 3.

Op-amps (ideal: infinite gain and input impedance, virtual short):

• Inverting amplifier gain −R_f/R₁; non-inverting 1 + R_f/R₁; voltage follower gain 1.
• Summing amplifier, difference amplifier, integrator v_o = −(1/RC)∫v_idt, differentiator v_o = −RC dv_i/dt.
• Slew rate limits the maximum undistorted frequency: f_max = SR/(2πV_m). Gain-bandwidth product is constant.
• First-order active filter cut-off f_c = 1/(2πRC); a Butterworth filter has a maximally flat passband and rolls off at 20n dB/decade for order n.

555 timer. Astable: f = 1.44/((R_A + 2R_B)C), duty cycle (R_A + R_B)/(R_A + 2R_B). Monostable pulse width T = 1.1RC.

Digital. Boolean algebra, K-maps, NAND and NOR as universal gates; a 2ⁿ:1 multiplexer has n select lines; flip-flops (SR, JK, D, T); a mod-N counter needs ⌈log₂N⌉ flip-flops; a Schmitt trigger has two thresholds (hysteresis).

Converters. An n-bit converter has 2ⁿ levels and resolution V_ref/2ⁿ (or V_FS/(2ⁿ − 1) for a DAC). Flash ADC: fastest, needs 2ⁿ − 1 comparators. Successive approximation ADC: n clock cycles per conversion. Dual slope ADC: slow, high noise rejection.

Worked example

Find V_dc for half-wave and full-wave rectification of a 20 V peak sine. Find the output of an inverting amplifier with R_f = 100 kΩ, R₁ = 10 kΩ and input 0.3 V. Find the frequency and duty cycle of a 555 astable with R_A = 1 kΩ, R_B = 10 kΩ, C = 0.1 μF, and the resolution of an 8-bit ADC with V_ref = 5.12 V.

import math

Vm = 20
print(f"half-wave Vdc = {Vm / math.pi:.4f} V, full-wave Vdc = {2 * Vm / math.pi:.4f} V")
print(f"inverting amplifier output = {-100e3 / 10e3 * 0.3:.2f} V")
RA, RB, C = 1e3, 10e3, 0.1e-6
print(f"555 astable f = {1.44 / ((RA + 2 * RB) * C):.2f} Hz, duty = {(RA + RB) / (RA + 2 * RB) * 100:.2f}%")
print(f"8-bit ADC resolution = {5.12 / 2 ** 8 * 1000:.0f} mV")

half-wave Vdc = 6.3662 V, full-wave Vdc = 12.7324 V
inverting amplifier output = -3.00 V
555 astable f = 685.71 Hz, duty = 52.38%
8-bit ADC resolution = 20 mV

Practice questions