Circuits II EE221 Unit 6 Instructor: Kevin D. Donohue Active Filters, Connections of Filters, and Midterm Project

Load Effects  If the output of the filter is not buffered, then for different loads, the frequency characteristics of the filter will change.  Example: Both low-pass filters below have f c = 1 kHz and G DC = 1 (or 0 dB).  Find: f c and G DC when a 100  load is placed across the output v o (t).  Result: f c = 11 kHz and G DC = 1/11 (or -21 dB) for the passive circuit, while f c and G DC remain unchanged for the active circuit.

Filter Order  The order of a filter is the order of its transfer function (highest power of s in the denominator). If the filter order is increased, a sharper transition between the stopband and passband of the filter is possible.  Example: For the two low-pass filters, determine circuit parameters such that f c is 100 Hz, and G DC is Plot transfer function magnitudes to observe the transition near f c.

First OrderSecond Order G DC = 1+R f / R 1 f c = 1 / (2  RC) For G DC = K =, f c = 1 / (2  RC) Formula not valid for any other value of K. Value of K was contrived so the cutoff would come out this way. For a general K value f c =  / (2  RC), where Transfer Function Results

Plot Comparison of Filter Order Effect w = [0:1024]*2*pi; s = j*w; h1 = (3-sqrt(2))./ (1 + (s / (2*pi*100))); h2 = (3-sqrt(2))./ (1 + (sqrt(2)*s / (2*pi*100)) + ( s / (2*pi*100)).^2); plot(w/(2*pi),abs(h1),'b-', w/(2*pi), abs(h2), 'b:') title('first order (-), second order (---)'); xlabel('Hz'); ylabel('gain') 3dB cut-off

SPICE Transfer Function Analysis  The simulation option for “.AC Frequency Sweep” with plot transfer function for simulated circuit. The frequency range (in Hz) must be selected along with plot parameters such as log or linear scales. Both the phase and magnitude can be plotted if requested. The input can be a voltage or current source with amplitude of 1 and phase 0.  Selection of the frequency range is critical. If a range is selected in an asymptotic region (missing the dynamic details of the transfer function) the plot will be misleading. The range can be determined by looking at large scale plots and making adjustments. Selecting a large range on a log scale may make it easier to identify the frequency range where change is happening, and then a smaller range can be selected to better show the details of the plot.

Spice Example :  Design the second order LPF so that it has a cutoff at 3.5 kHz with a gain of  Verify the design with a SPICE simulation. The key design equations become: So let C = 0.01  F and R f = 10k . This implies R = 4.55k  and (K-1)R f = 5.86k 

SPICE Results (Plot range 10 to 10 MHz)  The magnitude plot in dB. Crosshair marker near 3 dB cutoff (What is happening near 100kHz)?

SPICE Results (Plot range 10 to 10 MHz)  The phase plot in degrees. Crosshair marker near 3 dB cutoff (What is happening near 100kHz)?