## 5 Simulation and Experimental Results
### The Electronically Tunable VM Biquad  
As shown in Figure 2, the capacitors C\({}_{1}\) and C\({}_{2}\) were chosen as 2.2 nF and the bias currents were set to I\({}_{\text{B1}}\) = I\({}_{\text{B2}}\) = I\({}_{\text{B3}}\) = I\({}_{\text{B4}}\) = 200 \(\mu\)A (that is, g\({}_{\text{m}}\) = 2 mS). This setting has been designed for LPF, BPF, IBPF, IHPF, BRF, and APF responses, with f\({}_{\text{o}}\) = 144.7 kHz and Q = 1. Hence, the simulation and measurement functions of the LPF (V\({}_{\text{o1}}\)), IBPF (V\({}_{\text{o2}}\)), and BRF (V\({}_{\text{o3}}\)) in Part I are depicted in Figures 6-8, respectively. Figures 9-13 represent the simulated and measured functions of the LPF, BPF, IBPF, IHPF, and APF in Part II, respectively. The power consumption for simulation and measurement is 0.92 and 0.96 W under \(\pm\)15 V of supply voltage,  
Figure 8: Comparison of BRF experimental response, simulated response, and theoretical response in Part I.  
Figure 10: Comparison of BPF experimental response, simulated response, and theoretical response in Part II. Figure 9: Comparison of LPF experimental response, simulated response, and theoretical response in Part II. Figure 11: Comparison of IBPF experimental response, simulated response, and theoretical response in Part II. Figure 12: Comparison of IHPF experimental response, simulated response, and theoretical response in Part II. Figure 13: Comparison of APF experimental response, simulated response, and theoretical response in Part II. To illustrate the tunable property of natural frequency, f\({}_{\rm o}\), without affecting the Q, the bias currents \(\rm I_{B1}=I_{B2}=I_{B3}\) were given as 100, 200, and 300 uA respectively, while keeping \(\rm C_{1}=C_{2}=2.2\) nF and \(\rm I_{B4}=200\) uA. The simulation and measurement responses of the BPF on the V\({}_{\rm o1}\) output terminal corresponding to different DC bias currents are shown in Figure 14, where V\({}_{\rm i3}=\rm V_{in}\) and V\({}_{\rm i1}=\rm V_{i2}=\rm V_{i4}=0\). As depicted in Equation (9), Q can be used to adjust the transconductance gain, g\({}_{\rm m1}\), without affecting the f\({}_{\rm o}\). The feature of varying the Q without affecting the f\({}_{\rm o}\) is shown in Figure 15. Q varies (Q = 1, 1.5, and 2) when f\({}_{\rm o}\) is maintained at 144.7 kHz. In Figure 15, the I\({}_{\rm B1}\) was given as 200, 300, and 400 uA respectively, while keeping \(\rm C_{1}=C_{2}=2.2\) nF and \(\rm I_{B2}=I_{B3}=I_{B4}=200\) uA. To verify the dynamic range, the proposed biquad was tested by repeating simulation of the sinusoidal input signal at f\({}_{\rm o}=144.7\) kHz. Figure 16 shows the input dynamic range of the BPF on the V\({}_{\rm o3}\) output terminal when only V\({}_{\rm i4}\) is applied to the input signal, which indicates an amplitude of 60 mV\({}_{\rm PP}\) (peak-to-peak) without signification distortion. The total harmonic distortion (THD) result for the BPF response is shown in Figure 17. From Figure 17, it can be obtained that the THD is about 3.92% when the input signal increases to 80 mV\({}_{\rm PP}\). Figure 18 shows the measurement of the BPF response, which can be extended to an amplitude of 60 mV\({}_{\rm PP}\) without signification distortion. Figure 19 shows the simulation output noise of the BPF versus frequency. As shown in Figure 19, the maximum output noise reaches 7.937 nV\(/\sqrt{\rm Hz}\). Hence, the output noise was small and did not affect the proposed filter. Figure 14: Gain characteristics of the BPF with different f\({}_{\rm o}\). Figure 15: Gain characteristics of the BPF with different Q.  
Figure 10:0 Time-domain BPF input and output voltage signals. Figure 10:1 THD variations of the BPF against applied input voltages. Figure 10:2 Time-domain BPF input and output experimental voltage signals. To show the linearity of the biquad proposed in Figure 2, a 1 dB power gain compression point (P1 dB) of the IBPF response has been measured.