ENG 100 Pre-Lab #4Operational Amplifiers as BuffersA common application of op amps is to use them as “buffers” between circuits; they isolate different sections of a circuit. If a circuit has two sections, A and B, with respective transfer functions of HA(jw) and HB(jw), the overall transfer function of these two circuit sections in series with a unity-gain buffer between them is

HTOTAL(jw) = HA(jw) HB(jw)

A. 2nd-order bandpass with buffer: For the 2nd-order RC circuit shown below:

VOUT

+

–

C

C

R

VIN

+

–

R

+

–

Let R = 1500 W = 1.5 kW, and let C = 0.01 mF.

1. Derive the transfer function, w0, and Q. Bandpass form is Kw0s / (s2 + s(w0/Q) + w02).

2. Calculate the output amplitude, phase and time delay at each of the following frequencies (in Hz; these represent 2 logarithmically-spaced points per decade, from 100 Hz to 1 MHz):

100, 316, 1000, 3160, 10 000, 31 600, 100 000, 316000, 1 000 000

Notice that this circuit is the same as for Lab #3, only with a buffer isolating the two RC sections.

Record the results in a table. Plot the amplitude (in dB) versus frequency (Hz) and the phase (in degrees) versus frequency (Hz). Use a log scale for the frequency axis (Hz), and a linear scale for the dB and degree scales. Matlab, Excel, Mathematica, etc. are all okay to use; plotting by hand is also okay.

B. 4th-order bandpass Audio Filter: For the RLC circuit shown below:

L1

R1

C1

R4

R3

R2

C2

L2

VOUT

VIN

+

–

+

–

+

–

1. Determine the transfer function (Hint: For both the input and output circuits, just use the impedance divider formula. You can do them separately because the op amp isolates them from influencing each other.)

2. Design an audio bandpass filter using the constraints below:

2nd-order lowpass form is Kw02 / (s2 + s(w0/Q) + w02).

2nd-order highpass form is Ks2 / (s2 + s(w0/Q) + w02).

Lowpass Filter Stage: Let f0 = 15.9 kHz, Q=1, L1=10 mH; calculate values for R1 and C1. (Hint: Using the lowpass transfer function form, find w0 from f0, find C1 from w0 and L1, find R1 from w0/Q and L1.)

Op Amp circuit: Let R4 = 1 kW, set gain = 26 dB; determine the value for R3.

Highpass Filter Stage: Let Q=1, L2=100 mH; calculate values for R2 and C2 such that the magnitude (amplitude) for this stage is -19 dB lower than the high-frequency gain.

(Hint: While it is possible to do this with algebra, it may be easier to do this iteratively: Pick a possible value for f0 for this stage — try 200 Hz for a start — and see what the transfer function for this stage yields for the gain at 60 Hz; remember to convert from f0 to w0. Change f0 as needed to get -19 dB amplitude response at 60 Hz. Then use the figure you get and the value of L2 to get C2 and R2 from the standard highpass function form.)

C. Your PreLab Report

The TA may ask you to hand in the pre-lab, or he may check your pre-lab work by coming to your station while you work. Don’t leave until the TA has seen your pre-lab!

You should have stapled and ready for view:

A. The derivation, tabular data, and plots for the first circuit A,

B. The derivations and design values for circuit B.