6. Signal Generators

A signal generator produces a known stimulus to apply to a circuit under test. The output's quality (purity, accuracy, range) determines what you can measure: if your generator drifts, your bandwidth measurements drift; if it has harmonics, your distortion measurements include the source's distortion.

6.1 Wien-bridge sine oscillator

The classic audio-frequency sine generator is the Wien bridge oscillator. It uses an op-amp with positive feedback through a Wien network:

       ┌──── R ─┬─── C ───┐
       │        │         │
       ▼        ▼         ▼
   to op-amp  to op-amp  ground
   (+)         (−)
       
   Frequency: f = 1/(2π R C)

Positive feedback through the RC network at $f_0 = 1/(2\pi RC)$ has gain 1/3; the op-amp must therefore have closed-loop gain exactly 3 to oscillate. The amplitude-stabilization trick is the brilliance of the design: a thermistor (or sometimes a small incandescent lamp) in the feedback path provides automatic gain control. As output amplitude grows, the thermistor heats up, its resistance shifts, and gain drops back to exactly 3. The result is a remarkably clean sine, often $-100$ dB harmonic distortion.

The Wien-bridge with thermistor was the foundation of the original Hewlett-Packard 200A audio oscillator, the product that founded HP itself in 1939. The thermistor was the crucial innovation; with it, HP could undercut competitors by an order of magnitude in price while delivering better distortion specs.

6.2 Function generators with DDS

Modern function generators are digital. Direct Digital Synthesis (DDS) uses a phase accumulator, a sine lookup table, and a DAC:

   ┌────────────┐    ┌──────────┐    ┌─────┐
   │ Phase      │ ── │ Sine     │ ── │ DAC │ ── output
   │ accumulator│    │ lookup   │    └─────┘
   └────────────┘    │ (ROM)    │
        ▲             └──────────┘
        │
   Tuning word M
   (added to accumulator
    at every clock cycle)

Each clock cycle, the phase accumulator (an N-bit register) increments by tuning word $M$. The high bits of the accumulator address a sine lookup ROM, whose output drives the DAC. The output frequency is: $f_{out} = \frac{M \cdot f_{clk}}{2^N}$

For $N = 32$ bits and $f_{clk} = 100$ MHz, the frequency resolution is $f_{clk}/2^{32} \approx 0.023$ Hz. Tunable in milli-hertz steps, glitch-free, and absolutely repeatable: the same tuning word always produces the same frequency.

DDS supplanted analog oscillators because of this exactness. Examples: Rigol DG1000Z, Siglent SDG2000X, Keysight 33622A. They typically generate sine, square, ramp, pulse, noise, and arbitrary waveforms; bandwidth from a few MHz on entry-level units to GHz on top-end.

6.3 Pulse generators

A pulse generator produces edges with controlled width, period, amplitude, and rise/fall time. Used heavily for digital test (clocking sequential logic, generating reset pulses, characterizing latch behavior). Specifications matter: the transition time (the rise time of a fast edge) determines the frequency content of the pulse. A 1 ns rise time has frequency content out to roughly 350 MHz (using $BW \approx 0.35/t_r$, derived in the scope section below).

6.4 Random noise generators

Generate a known-statistics random signal: white noise (flat power spectral density) or pink noise (1/f shaped). Used for noise figure measurement, dithering, jitter testing, and sometimes to seed cryptographic randomness tests. A noise generator inside a security testing setup can deliberately introduce noise to test the resilience of countermeasures.

6.5 Sweep generators

A sweep generator linearly (or logarithmically) varies its output frequency over time. Paired with an oscilloscope or spectrum analyzer, you can plot the frequency response of a filter, an amplifier, or a transducer. Sweep generators were classic gear; today an AWG or function generator usually has sweep mode built in, and you might pair it with a network analyzer for more rigorous results.

6.6 Arbitrary Waveform Generators (AWG)

The Swiss army knife of signal generation. An AWG plays back any waveform stored in memory. You upload a sample-by-sample description (often via USB, sometimes via direct waveform editor); it clocks samples out through a DAC. A high-end AWG (Keysight M8195A, Tektronix AWG70000) can play back samples at up to 25 GS/s with 8-10 bit vertical resolution.

For hardware security: you can build an arbitrary glitch waveform (a precise sub-microsecond voltage dip on a target's power rail) and play it back synchronously to a target's clock. This is exactly how voltage-glitch fault-injection benches drive the chip into faulting an instruction. The ChipWhisperer platform's glitch generator is a small AWG-like circuit.