Grounded resistor tunes oscillator

To vary the frequency of any sine-wave oscillator, you should use a pair of ganged variable resistors, and you should thoroughly match their characteristics over the entire variation range to satisfy the oscillator's balancing conditions. This restriction leads to problems in the tuning range and high cost, thereby limiting the range of applications. The sine-wave oscillator in Figure 1 is free of the cited disadvantage. You can tune it over a wide frequency range using only variable resistor R1. The oscillator requires no balancing, so no matching problems arise. The variable resistor connects to ground, an advantageous fact in many applications. Like most classic sine-wave RC oscillators, the implementation comprises an operational amplifier, IC2, with two feedback loops. One loop is a frequency-independent, positive-feedback loop using two fixed resistors, R2 and R3, in this example. The other loop is frequency-dependent. This loop H(s)= s2 + sv0d1+ v02 divide s2 + sv0d0+ v02 uses capacitors C1 and C2; variable resistor R1; and a single-pole, double-throw analog switch, IC1, driven by a periodic sequence of square-wave pulses applied to the SW input.
Assuming a switching frequency, FS=1/T, much higher than the oscillation frequency and assuming that the pulse width, t , is half the switching period (t=0.5T), the approximate voltage transfer function of the frequency-dependent feedback loop is:where v0 = 1/2R=C1/C2 is the oscillation frequency, d0==C1/C2+2=C2/C1 , and d1=2=C2/C1 . Using this function and assuming the transfer coefficient of the positive-feedback circuit to be g=R2/(R2+R3), you obtain the oscillation condition in the form g>d1/d2=2=C2/C1/(2=C2/C1 +=C1/C2). The oscillation condition does not depend on R1. It thus becomes obvious that controlling grounded resistor R1 results only in the variation of the oscillation frequency and does not affect the condition for oscillation. This situation means that you can tune this oscillator over a wide range of frequencies, preserving the output waveform.

In this sine-wave oscillator, the output frequency is dependent only on the value of the grounded resistor R1.

PSpice simulations prove the possibility of tuning the oscillation frequency over three decades (20Hz to 20kHz) by varying R1 from 1.2 M½ 1.2 k½. This design uses an LT1361 (www.linear.com) for IC2, R2=1k½, R3=4.9k½, C1=10nF, C2=1 nF, and FS=500 kHz. The output-voltage amplitude is 3.2 to 3.3V. The total harmonic distortion in the 0- to 100kHz band does not exceed 3%. It's useful to note that, because the oscillation frequency is proportional to the conductance of the variable resistor (G1=1/R1), you can use the oscillator as a linear, wideband conductance-to-frequency or resistance-to-period converter.