The circuit in Figure 1 is based on a classic GIC (generalized impedance converter). The sine-wave-oscillator circuit has inherent amplitude stabilization and normally operates from dual power supplies. However, if you connect an additional resistor, R_{CC}, to V_{CC}, you can operate the circuit with one supply (with V_{EE} = 0 V). You can adjust the oscillation frequency by varying R_{1}. R_{COMP} ensures oscillation and does not affect the oscillation frequency. The remaining passive components are four equal-value resistors, R, and two capacitors, kC and C/k, where k is a scaling factor. This modification of the classic GIC structure incorporates an additional resistor, R_{N}, between both inverting op-amp inputs. The GIC topology has excellent high-frequency properties and thus finds extensive use in active-filter circuits. The GIC structure can simulate a grounded inductance or a grounded FDNR (frequency-dependent negative resistance).

Figure 1. |
A GIC-based resonator provides inherent amplitude control and low distortion. |

You can explain the function of the circuit by starting with the GIC input impedance at either Port 1 or Port 2. A straightforward analysis of the circuit yields the input impedance at Port 1:

Note that, for R_{COMP} = R_{N}, the expression for Z_{IN1} represents the input impedance of an ideal FDNR. The FDNR, together with an ohmic shunt resistance from Port 1 to ground, forms a tuned circuit with the inherent capability to oscillate. In reality, however, the oscillation would die out because of parasitics arising from lossy capacitors and imperfect amplifiers. The circuit in Figure 1 compensates for these losses by using the second portion of Z_{IN1}, representing a negative capacitance for R_{COMP} < R_{N}. In practice, you should choose R_{N} = R and a resistor ratio, R_{COMP}/R, close to unity (for example, R_{COMP}/R = 0.95 to 0.98). If you perform the analysis at Port 2 of the circuit, the input impedance, Z_{IN2}, represents an ideal inductance in series with a negative resistor. Shunting this impedance with a capacitor-resistor branch (C/k and R_{COMP} in Figure 1) creates a lossless LC tank circuit. This tank circuit can oscillate if you satisfy the condition R_{COMP} < R. The circuit starts reliably and oscillates at the following frequency:

For the circuit values in Figure 1, IC_{2} saturates, providing a clipped sinusoidal signal at V_{OUT2}. V_{OUT1} is a filtered version of that signal. Thus, no extra circuitry is necessary for amplitude stabilization. However, the quality of the sinusoidal signal at V_{OUT1} depends on the Q factor of the resonator circuit, as the following equation states:

For the values shown, a quality factor Q > 100 results with a capacitance scaling factor k = 4, C = 100 nF, and (R_{N} – R_{COMP}) = 50 Ω. V_{OUT1} provides a signal with a total harmonic distortion lower than 1% at f_{0} = 1 kHz. The peak-to-peak amplitude of the sinusoidal signal is approximately 1 V lower than the total supply-voltage span.