ECE 3235 Electronics IIActive Filter Circuits1. Single Amplifier Band Pass FilterECE 3235 Electronics IIExperiment # 10Active Filter Circuits1. Single Amplifier Band Pass FilterFigure 8.1 Single Amplifier Bandpass Filter.Figure 8.1 shows a single amplifier active filter circuit of the bandpass variety. It is alsocalled a Sallen-Key filter, after the discoverers of this topology, or a KRC filter because ituses R and C components, as well as a noninverting amplifier (whose gain is usuallydenoted by K, where K = 1 + Rb/Ra in the circuit shown). The components shown are fora center frequency of approximately 1 kHz.Wire up this circuit, after having measured all component values (with the exception ofthe potentiometer’s) accurately. Use a decade capacitance box for either C1 or C2 and adecade resistance box for R. Adjust so that C1 and C2 are equal, and so that R = R1R2. Then compute the value of required amplifier gain K for Q = 2 from equation (2)below (equation 1 is given for future reference):Then, noting thatCompute the required value of Ra. Take your 50K potentiometer from the circuit (youdo not have to physically remove it, just remove the ground wire) and use your DMM inits ohmmeter function to adjust the potentiometer to the required value. (Be precisehere!) Now, taking care not to alter the setting of the potentiometer, wire it back into thecircuit.Connect the sinusoidal source to the input at a frequency of approximately 1 KHz and alevel of about 1V peak-to-peak. Observe the output with your oscilloscope as youslowly change the frequency up and down (around 1 KHz). Can you find a frequency fowhere the gain peaks? Attach your frequency counter and DMM (on an ac voltage scale)to the output, and measure the peaking frequency precisely. Now, adjust the input levelof your circuit so that the output reads 100mV rms (Root Mean Square) precisely on yourDMM at the peaking frequency. Then find the two frequencies (fu above and fL belowthe peaking frequency, respectively) where the output level drops to 70.7mV rms. Compute your experimental Q from the following expressionNow change the input waveform to a square wave at an initial frequency of 100 Hz (atthe same amplitude as before), but vary the frequency so that you see a complete periodof the output waveform accurately. It should be a damped sinusoid. (It might be ofbenefit here to learn to use the “delayed sweep” mode of your scope). Measure theamplitudes of the first and second peaks adjacent (+ and – excursions) of the outputwaveform. You may adjust the input level by a small amount to make thesemeasurements easier. Use these values in equation (5) below to compute an experimentalvalue of Q from this step response test:whereMeasure the period of the damped oscillation (or “ringing”). Again, it might proveadvantageous to use the delayed sweep mode of your oscilloscope, and then compute thepeaking frequency from equation (7) below:Where T is the period you have just measured, and Q is the value of Q’exp in equation (5)above.Repeat the entire procedure above for a desired Q of 10. Note that you must be veryprecise in your measurements, particularly in the adjustment of the 50 K potentiometer.2. Multiple Amplifier Active FilterFigure 8.2 depicts a multiple amplifier active network known as a “state variable” filter.Figure 8.2 A State Variable Active Filter Circuit.Wire this circuit, after having measured all component values accurately.In this circuitCompute the value of Ra required to achieve a Q of 2. Then select the nearest standardvalue and measure this value using your DMM in its ohmmeter function. Carefully wireit into the circuit. Now repeat the frequency and time response measurements of Part 1 [1]. Then select a new value of Ra to achieve a Q of 5 and repeat these measurements.3. Cadence SimulationSimulate the two circuit in Cadence and compare your simulation results with those thatyou have measured.[1] This circuit is somewhat prone to oscillation. If it does oscillate, carefully bypass the positive andnegative supplies using a high quality (non-electrolytic) capacitor of 0.01 microfarad, or larger. If attachingan oscilloscope or ac meter to the output causes oscillation to occur, place a 1 KΩ resistor between thecircuit and the instrument.Compound Problems(A) Derive equations (1) and (2).(B) Express Q in terms of Ra and Rb. Then plot Q versus Ra using MS Excel, carefullylabeling your axes. Plot Q on the vertical axis and Ra on the horizontal axis, assuming Rb= 100 K.(C) Compute the value of Ra required for a Q of 20 (assuming that Rb = 100 K.) Then assume that Ra decreases by 1%, and compute the resulting value of Q. On thebasis of your result, do you consider the single amplifier KRC circuit a good one for highQ applications? Why?(D) Using the fact that the general second order bandpass transfer function (for anyrealization) isShow that the steady state sinusoidal frequency response peaks (has a maximum) at  =0. Hint: Consider H(j)2 and “manipulate” the result. From your result, obtain thepeak gain Hp = H(jo).(E) By computing the upper and lower corner frequencies (u and 1, respectively),show that equation (4) is valid.(F) Derive the transfer function H(s) = Vout(s)/Vin(s) for the state variable filter, andverify equations (8) and (9).(G) Compute the value of Ra required for a Q of 20, assuming R = 100 KΩ. Then letRa increase by 1%, and compute the resulting Q. Is this filter circuit better or worsethan the KRC circuit for their peak-to-peak values? Also, carefully measure the value ofRb without disturbing its setting. (Simply disconnect one terminal from the circuit