Format of Filter Quiz (2014 update)

You will be asked to design a VCVS bandpass or band-reject filter. Your answer will be based on the lecture and online lecture notes on filters, reading the first part of chapter 5 of Horowitz and Hill, and the Matlab function VCVSfilt4.m in a script set up you. For the quiz you should have access to a computer running Matlab; you can also refer to any notes you like.

We will set you up with a Matlab script template in a folder on the Matlab path in a folder like:
\MatlabR12\Work\FiltQuiz.
Your script will call function VCVSfilt4 in the solution to your problem. VCVSfilt4 is a Read Only file that solves for R1=R2, K, and Vout(freq) when you supply it with a frequency range, center frequency, capacitance, filter type and filter name. In Matlab type at the command line >>
help VCVSfilt4
to

The specifications in your call to design will
* tell you whether it's bandpass or band-reject filter
* imply that Bessel, Chebyshev or Butterworth would be the "type" of filter
* set limits on gain for the edges of the pass or reject region
* set a limit on gain for the middle of the freuency pass region
* tell you the size of all the capacitors you can use in the design
* tell you that the gain-setting "K" resistors R are 10K ohms
* ask you to show the spectrum (plotted in VCVSfilt4) of the gain with log freq vs linear gain
* ask you to draw out the circuit, using no more than a certain number of op amps, and showing all resistance value and
showing what sub-circuit joins the LP and HP parts of the filter.

For the sake of the Filter Quiz, all gains will be non-zero. In fact the response of a filter to a sinusoid based calculated by the node admittance matrix method results in complex numbers at each frequency. The gain the magnitude of the complex number, which will always be a positive number; where it lands in the complex plane will be determined by the phase angle of the response. In forming the answer to a band-reject filter if you (for some odd reason) subtract one filter response from another and end up with negative numbers, you must take the abs value of that answer as the "gain."

Another way to think about sinusoidal input and gain: as the peak-to-peak response of the resulting waveform--again a number that is always non-negative...

If you can't meet the specs with 1 LP and 1 HP filter consider putting 2 filters in series to increase the sharpness of a cutoff.

Your answer--script, spectrum and circuit diagram--must be presented in person to JDD or a TA for inspection and approval.

Examples of filter quizzes:

% design a maximally sharp bandreject filter such that
% at 36Khz the gain is greater than 1.25 and
% at 200KHzKHz the gain is less than 0.3
% and at 650KHz the gain is greater than 1.1
% no gain in spectrum greater than 2.5
% use only 0.003 muF capacitors
% gain setting resistor is R = 10K for VCVS template on p. 274 of H&H
% show spectrum meeting specs in form of semilogx plot with linear gain on y axis
% draw a circuit diagram of LP and HP components and
% show how the LP and HP are combined or connected together for a
% final Vout whose gain w.r.t. Vin is spec'd above
% include ALL resistance values in ohms. no more than 14 op amps allowed.
% if spectrum is valid for 3 consecutive tries of res_flg == 1, then +2 point bonus.

% design a maximally sharp gain curve bandpass filter such that
% at 24Khz the gain is less than 0.2 and
% at 95KHz the gain is less than 1.2
% and at 580KHz the gain is less than 0.22
% no gain in the pass band greater that 2.7

% use only 0.05 muF capacitors
% gain setting resistor is R = 10K for VCVS template of p. 274 H&H
% show spectrum meeting specs in form of log freq vs gain plot
% draw a circuit diagram of LP and HP components
% show how the LP and HP are combined or connected together for a
% final Vout whose gain w.r.t. frequency is spec'd above
% include ALL resistance values in Ohms. no more than 10 op amps allowed.
% if res_flg == 1 and the spectrum is valid for 3 consecutive tries, then 2 point bonus

Real Resistor bonus. If you set the last argin of VCVSfilt4--res_flg--to 1 the program will call function Nearest_Rstd which will find the nearest resistor in a bin of 13 resistors per decade; it will then randomly alter that resistance RR by +/- 5%; it will also alter the given capacitance CC by +/- 20%; if your spectrum still meets the specs after running res_flg == 1 3 times in a row, you will receive a 2 point bonus (on the A-path).

Filter Quiz answers given after Thanksgiving will receive half credit on the A-path.