Diode Circuits, Amplifiers, Op-Amps, Active Filters and Digital Logic
2. Oscillators, feedback amplifiers, op-amps and active filters
A sinusoidal oscillator is an amplifier with positive feedback engineered to satisfy the Barkhausen criterion at exactly one frequency: loop gain magnitude equal to 1 and loop phase shift equal to 0 (or a multiple of 360 degrees) — below this the oscillation dies out, above it grows until non-linearity (saturation) limits the amplitude, and exactly at it a sustained sinusoid results. An ideal operational amplifier has infinite open-loop gain, infinite input impedance and zero output impedance, which is the basis of the 'virtual short' approximation used to analyse every standard op-amp circuit: with negative feedback, the two input terminals are assumed to sit at the same voltage even though no current actually flows between them.
| Circuit | Function |
|---|---|
| Inverting/non-inverting amplifier | gain set purely by external resistor ratio, negative feedback |
| Integrator | output proportional to the time-integral of the input |
| Differentiator | output proportional to the rate of change of the input |
| Comparator | open-loop (or positive feedback), output saturates high or low based on which input is larger |
3. Combinational and sequential logic, multiplexers and demultiplexers
A combinational circuit's output depends only on its present inputs, with no memory of the past (adders, decoders, multiplexers, encoders), while a sequential circuit's output depends on present inputs AND on a stored internal state (flip-flops, counters, registers), which is exactly what gives it memory — the state itself is held by feedback inside the circuit (typically a pair of cross-coupled gates or a clocked latch), not by any external component. A multiplexer selects one of several data inputs to route to a single output based on select lines (2^n inputs need n select lines), and a demultiplexer does the reverse, routing a single input to one of several outputs — the two are functional inverses of each other.
| Type | Key behaviour |
|---|---|
| SR | both inputs high simultaneously is a forbidden (invalid) state |
| D | output simply follows the D input at the clock edge, no forbidden state |
| JK | resolves SR's forbidden case: both inputs high makes the output TOGGLE |
| T | output toggles on every active clock edge when T is high; holds when T is low |
4. Schmitt triggers, sample-and-hold circuits, and A/D and D/A converters
A Schmitt trigger is a comparator with positive feedback, giving it two distinct switching thresholds (hysteresis) instead of one — it switches high going up only above the upper threshold, and switches low going down only below the lower threshold. This is precisely what makes it immune to a noisy signal that hovers around a single simple threshold and would otherwise cause many spurious extra transitions on a plain comparator; a Schmitt trigger is the standard 'clean up a noisy digital edge' building block for exactly this reason.
A sample-and-hold circuit acquires (tracks) an analog input during a brief sample period, then freezes (holds) that value on a capacitor while the rest of the conversion circuitry does its work — every practical ADC needs one ahead of it, because most ADC architectures need the input to stay constant for the whole conversion time, while a real-world signal keeps changing. The specific problem this solves is called aperture error: without a hold, a changing input during conversion would make the converted digital code correspond to no single instant of the actual waveform.
| Type | Speed | Complexity/cost |
|---|---|---|
| Flash (parallel comparator) | fastest — one clock cycle | 2^n - 1 comparators, doubles with each added bit |
| Successive approximation (SAR) | moderate — n cycles for n bits | one comparator, one DAC, standard general-purpose choice |
| Dual-slope (integrating) | slowest | very simple, high accuracy, immune to component drift |
Key takeaways
- A clipper genuinely changes a waveform's shape (discarding part of it); a clamper preserves shape exactly and only shifts its DC level — the two are tested by exactly this distinction.
- A sinusoidal oscillator satisfies the Barkhausen criterion, loop gain = 1 and loop phase = 0 (or a multiple of 360 degrees), at exactly the oscillation frequency.
- A practical differentiator needs a series resistor to cap its otherwise unlimited high-frequency gain; an integrator has no such problem since its gain falls, not rises, with frequency.
- JK's J=K=1 toggle case exists specifically to give a deterministic outcome for SR's forbidden, race-prone S=R=1 case.
- Flash ADC trades comparator count for maximum speed; SAR trades a fixed n-cycle latency for moderate hardware (the default choice); dual-slope trades speed entirely for drift-immune accuracy.
Practice questions (9)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
A clamper circuit, as distinct from a clipper, is characterised by
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Answer: B — shifting the waveform's DC level while preserving its exact shape
A clamper's diode-capacitor network shifts the entire waveform up or down to a new DC reference without altering its shape at all — a clipper is the one that discards part of the shape, and neither device is a rectifier or an amplifier by itself.DC bias analysis and AC small-signal analysis of a BJT amplifier are always kept separate because
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Answer: B — DC sources are zeroed and reactive elements are treated differently (short or open) in the two analyses
The two analyses use genuinely incompatible simplified models — DC sources become zero for AC small-signal analysis while coupling/bypass capacitors become shorts, whereas for DC bias analysis it is the opposite (capacitors are open, DC sources are active) — so combining them in one pass is not meaningful; every practical amplifier IS biased and driven with AC simultaneously, just analysed in two separate steps.The Barkhausen criterion for sustained sinusoidal oscillation requires
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Answer: B — loop gain magnitude exactly 1 and loop phase 0 (or a multiple of 360 degrees)
Barkhausen's criterion is exactly loop gain magnitude 1 (unity) with loop phase shift 0 degrees (or a multiple of 360) at the oscillation frequency — greater than 1 causes growing amplitude until saturation limits it, less than 1 causes the oscillation to die out, and 0 loop gain (option D) cannot sustain anything at all.A practical op-amp differentiator circuit adds a small resistor in series with its input capacitor chiefly to
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Answer: B — cap the otherwise unlimited high-frequency gain and improve noise immunity
An ideal differentiator's gain rises without bound as frequency increases, amplifying high-frequency noise and risking instability; the added series resistor caps this gain at high frequency to a safe, finite value, at some cost to ideal differentiating behaviour at the very highest frequencies.Which of the following are correctly true of combinational versus sequential circuits?
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Answer: A — A combinational circuit's output depends only on present inputs.; B — A sequential circuit's memory is held by feedback inside the circuit, not by an external component alone.
The first two are correct definitions. A multiplexer and demultiplexer are functional INVERSES of each other (many-to-one versus one-to-many), not the same function, and a decoder is a combinational circuit (its output depends only on the present input code, with no stored state) — not sequential.In a JK flip-flop, the input combination J=1, K=1 at an active clock edge causes the output to
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Answer: B — toggle to the opposite of its previous state
J=K=1 is specifically defined to make the JK flip-flop toggle, which is exactly the case that was left forbidden and race-prone in the simpler SR latch — this deterministic toggle behaviour is the entire reason JK is preferred as the general-purpose flip-flop.A Schmitt trigger differs from an ordinary comparator chiefly in that it has
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Answer: B — two distinct thresholds (hysteresis), immune to noise around a single level
A Schmitt trigger's positive feedback creates two distinct switching thresholds (upper and lower), so a noisy signal hovering around a single level does not cause spurious multiple transitions the way it would on an ordinary single-threshold comparator — this hysteresis is precisely its defining feature.A sample-and-hold circuit is placed ahead of an ADC chiefly to prevent
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Answer: B — aperture error from the input changing during the conversion time
Without a hold, an input that keeps changing during the finite conversion time would make the resulting digital code correspond to no single well-defined instant of the waveform — this is aperture error, distinct from quantisation error (a resolution limit) and aliasing (a sampling-rate issue handled upstream by an anti-aliasing filter).A flash ADC resolves n bits using 2^n - 1 comparators. For n = 4 bits, the number of comparators needed is ___
Numerical answer — type the value.
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Answer: 15
2^4 - 1 = 16 - 1 = 15 comparators — the count doubles roughly with each added bit, which is exactly why flash converters are used only for a small number of bits despite being the fastest architecture available.