Op-Amps & Analog Circuits

Op-Amps & Analog Circuits

Op-amp fundamentals, comparators, Schmitt triggers, charge pumps, and practical circuit analysis.

List and explain ideal op-amp characteristics.
  • Infinite open-loop gain: A_OL → ∞
  • Infinite input impedance: No current flows into input terminals.
  • Zero output impedance: Can drive any load without voltage drop.
  • Infinite bandwidth: Gain is constant at all frequencies.
  • Zero input offset voltage: V_out = 0 when V+ = V−.
  • Infinite CMRR: Perfectly rejects common-mode signals.
  • Infinite slew rate: Output can change instantaneously.
  • Zero noise: No internally generated noise.
Draw and explain a non-inverting amplifier.
Input connects to the non-inverting (+) terminal. A resistor divider (R₁ from output to inverting input, R₂ from inverting input to ground) provides negative feedback.

A_v = 1 + R₁/R₂

The gain is always ≥ 1, input impedance is very high (ideally infinite), and the output is in phase with the input.

How does finite open-loop gain affect a non-inverting amplifier?
With finite open-loop gain A_OL, the actual closed-loop gain becomes:

A_CL = A_OL / (1 + A_OL · β)

where β = R₂/(R₁+R₂). The actual gain is always less than the ideal (1+R₁/R₂), with a gain error of approximately 1/(A_OL·β). As frequency increases and A_OL rolls off, the gain error worsens and the circuit bandwidth is limited to GBW/A_CL.

Swap the op-amp polarity — derive the Schmitt trigger behavior.
Swapping polarity creates positive feedback: the resistor divider now feeds back to the non-inverting (+) input. This creates a Schmitt trigger (bistable comparator) with hysteresis. The two thresholds are:

V_TH = V_ref + (V_OH − V_ref) · R₂/(R₁+R₂)
V_TL = V_ref + (V_OL − V_ref) · R₂/(R₁+R₂)

The hysteresis band (V_TH − V_TL) prevents output oscillation from noisy input signals, which is why Schmitt triggers are essential for cleaning up noisy digital signals.

How does a comparator work?
A comparator is a high-gain open-loop amplifier optimized for switching speed. It compares two input voltages: if V+ > V−, the output swings to V_OH (logic high); if V+ < V−, it swings to V_OL (logic low). Unlike op-amps, comparators are designed for open-loop operation with fast slew rates, no internal compensation (for speed), and digital-compatible output stages.
How does an oscilloscope work?
A modern digital oscilloscope:

  1. The input signal passes through an attenuator and buffer amplifier for scaling.
  2. A high-speed ADC samples the signal at the set sample rate.
  3. Samples are stored in acquisition memory.
  4. A trigger circuit detects a specified event to synchronize the display.
  5. A DSP engine processes the data (measurements, FFT, averaging).
  6. The waveform is rendered on a display with calibrated time (x-axis) and voltage (y-axis) scales.
Circuit analysis: 1.8V clock through a charge pump — derive V_out.
Given V_in = 1.8V square wave, 50% duty cycle, with a Dickson-style charge pump:

  1. V_in goes HIGH (1.8V): First diode conducts, clamping V_node to approximately −0.6V (one diode drop below ground).
  2. V_in goes LOW (0V): Capacitor holds its charge, so V_node drops by 1.8V: V_node = −0.6 − 1.8 = −2.4V.
  3. Second diode conducts: V_out = V_node + V_f = −2.4 + 0.6 = −1.8V

Steady-state output is approximately −1.8V DC (a negative voltage generator).

When to use oscilloscope vs. logic analyzer?
  • Oscilloscope: Analog tool for observing signal shape, voltage levels, timing, rise times, ripple, noise. Use AC coupling to zoom in on ripple. Primary tool for mixed-signal debugging.
  • Logic Analyzer: Digital tool for capturing and analyzing digital signals — verifies frequency, duty cycle, protocol decoding, timing relationships between many channels. Cannot measure analog voltage levels.

For mixed-signal circuits, use the oscilloscope as the primary tool and the logic analyzer for correlating digital control signals.

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