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Standard variable capacitors seldom have a tuning range much over 10:1, measured as maximum capacity / minimum capacity. Since the resonant frequency is inversely proportional to the square root of capacitance, a variable capacitor with a 10:1 max:min ratio allows a frequency tuning range of square root (10) or just over 3:1.  It goes without saying, perhaps, that a laboratory audio oscillator variable over a 10:1 frequency range without band changing is preferable to one offering only a 3:1 tuning range.

In the most useful form, the two resistors, R1 and R2 are equal in value, as are the two tuning capacitors, C1 and C2 and thus the above equation has only R1 and C1 values. (If you look carefully at the 200CD schematic shown later on this page, however, you will see that C1 = 2*C2 and R1=0.5*R2. The 2x and 0.5x relationships cancel and result in the same performance as in the case where R1=R2 and C1=C2.)

Of critical importance, of course, is that the oscillator frequency is no longer related to the tuning capacitance by a square root. Rather, it's a direct inverse relationship. Hence, if the tuning capacitor has a 10:1 range, the oscillator likewise has a 10:1 tuning range. Each band on my 200CD, in fact, has a range exceeding 12:1, e.g., on the lowest band, one sweep of the dial takes the frequency from about 4.8 Hz to 65 Hz. 

How does this circuit work to sustain oscillation? The output of the second stage pentode is fed back to the first stage grid. Since there's 180 degree phase shift in each amplification stage, the net phase shift from the output stage to point "a" is 360 degrees. If, therefore the RC network R1/C1/R2/C2 has zero additional phase shift at a particular frequency, we have met one of the two Barkhausen criteria for oscillation; phase shift is an integral multiple of 360 degrees. (The second criterion is that the net gain >= 1 at the oscillation frequency. We can satisfy this by selecting component values and, of course, the negative gain stabilization feedback provided by lamp R3, as discussed below.)

With the 200CD, HP made a major revision to its audio oscillator design, as can be seen in the circuit fragment below. For our amplitude feedback purposes, note that the 200CD uses two series lamps, R13 and R14, 10 watt rating at 250 volts. The lamps have across them the AC signal voltage produced by the oscillator. R11 and R12 provide a level adjustment mechanism when the lamps are replaced.

If the oscillator output increases, Eb increases. Also, the lamp, R1, will increase in resistance thereby disproportionally increasing voltage Ea. Since the amplifier output is proportional to Eb-Ea, R1 introduces a stabilizing element, as Ea increases proportionally more than Eb.

But, where on this curve should the designer place the lamp's operating point? It turns out that the most desirable operating point is where the change in lamp resistance is maximum for a change in voltage--thereby providing the maximum negative feedback effect. In other words, the designer will select the point at where the derivative of the resistance versus voltage curve is a maximum. The figure below plots this derivative, showing both the derivative of the measured data (black) and the derivative of the curve-fitted 5th order polynomial (red curve).  Strictly speaking, these are not derivatives but rather differentials, as they are computed by taking numerical differences between measured values, but we'll ignore the difference. The noise spikes in the measured data are artifacts in the measured data. It's better to look at it as a smoothed curve and ignore the noise spikes.

The data shows the most sensitive part of the 10 watt / 250 V lamp is at about 2 volts, although the there is not too much change in the derivative over the range of 1 volt to 5 volts. In fact, the 200A schematic fragment shows 3.2 volts DC across the lamp. However, the 200A's lamp is not the one measured and, of course, the cathode has an signal frequency AC component as well. (The bypass capacitor C7, appears to be a small value capacitor intended to boost high frequency performance.)

If we plot the lamp resistance over the same range as a function of applied power, as suggested in the HPJ article, we see two linear ranges. The first range, with the blue line extension is close to a zero temperature coefficient resistor. There's so little power in this range (less than 0.5 milliwatt) that the filament temperature changes very little as the power changes. At around 5 milliwatts, the resistance picks up a second log-log linear relationship.

I don't have the 3 watt lamp used in the 200A oscillator, but I did pick up a 4 watt 120 volt "nightlight" lamp and collected the data presented below for it.