Bob Moog's 1965 patent (US 3,475,623) defined the sound of analog synthesis with a deceptively simple structure: four identical stages, each a differential pair of BJTs driving an emitter capacitor, cascaded with global feedback for resonance. Every subtractive synth voice you've ever heard through a "Moog filter" is a descendant of this topology.

The core stage is a long-tailed pair whose emitters share a capacitor to ground. The differential input voltage steers current through the capacitor, and the output is taken differentially from the collectors. Because the pair is biased by a common tail current I_bias, the transconductance g_m = I_bias/(2V_T) is linearly proportional to bias current. That's the whole trick: change I_bias, and every stage's -3dB frequency shifts together.

Cutoff frequency per stage: f_c = g_m/(2πC) = I_bias/(4πV_TC). At room temperature V_T ≈ 26mV. With C = 1nF and I_bias = 10µA, f_c ≈ 30kHz. Drop I_bias to 100nA and f_c falls to 300Hz. Since bias current is set by a control voltage through an exponential converter (a translinear V-to-I), you get 1V/octave tracking — the standard synthesizer control law.

Four stages cascaded give 24 dB/octave rolloff. Feeding the final output back to the input inverted, scaled by a resonance knob (typically 0 to 4), creates a peak at cutoff. At feedback gain = 4, the filter self-oscillates, producing a pure sine wave — the classic Moog resonance sweep.

Real-world example: the Minimoog Model D uses PNP pairs (2N3906-style) with 470pF caps and a bias current range of roughly 100nA to 20µA, giving 20Hz to 20kHz sweep. The exponential converter uses a matched dual transistor (LM394 or a monolithic pair) to hold 1V/oct across temperature — without matching, the top octave drifts wildly as the die warms.

Design gotchas:

• Signal level: the differential pairs are only linear for ±V_T ≈ ±26mV. Overdrive them and you get the characteristic Moog "saturation" — a musical feature, but a distortion nonetheless. Serious designs attenuate the input to ~20mVpp.
• Resonance kills bass: the classic ladder loses low-frequency signal amplitude as resonance rises (the feedback path removes energy). Many modern clones add a compensation path.
• Temperature: V_T drifts at +0.33%/°C. The exponential converter must be tempco-compensated with a +3300 ppm/°C resistor (a "tempco resistor") in the current-setting network.

Rule of thumb: for a ladder VCF with capacitor C, choose bias current I_bias ≈ 4πC·V_T·f_c,max. For 20kHz max with 1nF, that's about 6.5µA — a comfortable operating point.