Four operational amplifiers with two feedback loops are utilized to design an analog computer that is able to solve a second order differential equation that relates the applied input voltage signal to the output voltage of this circuit. A quick method using KCL is shown to compute and find the voltage transfer function and characteristic equation of this circuit. Assuming proper selection and biasing of Op Amp (good slew rate, low drift and low noise with proper bandwidth given desired application) this circuit has a DC gain of 4 (in steady state) and also operates well with sinusoids. For more circuit examples please see • Electrical Engineering... . For example for Audio signal processing application, we can try resistor R=1k and capacitor C=1nF. This circuit effectively is a second order lowpass filter with a transfer function of 4*(wn)^2/(S^2 + 2*zeta*wn*S + (wn)^2) where natural frequency wn=0.5/(R*C) = 500k rad/sec and damping factor zeta=3 which means this circuit is overdamped. If one volt DC voltage is applied at input, the circuit output voltage should smoothly reaches 4 volts at the output in roughly 50-60 micro seconds. As the second test we can apply 10 kHz sinusoidal voltage (with say amplitude 1 volt) at input and examine if the 10kHz sinusoid appears at the output with four times amplitude. It should because 3dB bandwidth or cutoff frequency of this filter is roughly 80000 radian per second (or nearly 15kHz) and hence 10kHz sinusoid is considered in-band for this circuit. Assuming the DC test and sinusoid test are passed then we can try other input waveforms.
23 сен 2024
