A CMOS inverter biased in its active region behaves like a transconductor with its positive input grounded. Determine the impedance of an inverter whose output is shorted to its input. Measure the transconductance by forming a voltage divider with this impedance and measuring the voltages v_x and v_y as shown above. Do the measurements at 5V, 6V, and 7V supplies. Also note the dc bias voltage of the self biased inverter.

Design the gm-C filter shown above for a resonant frequency of 5kHz and a quality factor of 2. Determine the transfer functions between the input and V₁ and V₂. Build the filter using only transconductors and capacitors. i.e. the resistor and the positive transconductor should be realized using only the inverters available on a 4069.

Measure the circuit and verify that it realizes the transfer functions given above. Filters can be measured by injecting sinusoidal inputs and observing inputs and outputs on 2 channels of an oscilloscope. Also, the phase difference between input and output can be gauged from X-Y plots, and the center frequency determined. Observe the step response by injecting a low frequency square wave to the filter.

Tune the filter using the power supply voltage and verify that it tunes as expected. The voltage V_bias in the input should be the bias of the self biased inverter.