Familiarity with operational amplifiers (OpAmps) and basic OpAmp circuits: inverting, non-inverting, summing amplifiers, Filters.
Operational amplifiers (OpAmps) are analog integrated circuits containing tens of transistors with well-matched elements designed to amplify the difference of two signal using a very high input impedance, a very low output impedance, and a very large open loop gain. The very high open loop gain makes them suitable for designing applications where the performance is almost impervious to the characteristics of the OpAmp. The main reason for designing OpAmps is the implementation of arithmetic operations in the analog world. Most of our applications are going to be based on the most popular one, the 741 OpAmp (though other OpAmps will be more suitable in many other situations).
All applications in Lab 1 are based on a negative feedback configuration. The output and the inverting input are connected to each other either directly, or in most cases through other components. We will also assume in our analyses that the OpAmp is almost ideal.
Two rules will then prevail:
You will note that the output voltage will be kept 1 to 2 volts (usually one to two junction drops) below VCC or above -VEE.
Analyze every circuit in this lab (just determine all the desired characteristics, such as the voltage gain, the input or output resistances, transfer function, wherever applicable), and simulate every circuit in Multisim using the measured values of the components that will be available during the implementation (not the nominal values). Every circuit must be implemented using the required suggested values, not the ones from the circuits presented in this document.
S. Franco "Design with Operational Amplifiers and Analog Integrated Circuits", McGraw-Hill 1988. Chapter 1.
Equipment needed from the stockroom: scope probe, resistance substitution box, leads.
The reading of the current I1, as shown in Figure Figure 1.1.1 would not be accurate if you conduct the same measurement while the output is driven to saturation, shown in Figure 1.1.2 This current confirms that the input resistance is 1kΩ.
This section regarding the inverting amplifier is to be conducted entirely through Multisim only.
Assemble a non-inverting amplifier with a gain of 10, and an input resistance of 100kΩ. Simulate your proposed circuit before you implement it and verify the two parameters (gain and input resistance using the same DC supply, and 1-V peak sinewave). Compare to your calculations and simulation results.
Answer the following question: what is the purpose of a unity-gain buffer?
Simulate only a two-input summing amplifier, similar but not necessarily using the same values as shown in Figure 1.1.4 with equal gain on both inputs. Test it with two waveform generators, first with the two frequencies equal, and then with the two frequencies 500 Hz apart from each other. In the first case, the sinewaves just add up, whereas in the second case, we achieve the equivalent of what we call Double-Side Modulation (DSB), with the sinewave having the difference of frequencies acting as a message signal, and the sinewave having the sum of the two frequencies acting as a carrier.
In the following Matlab example, assume that half of the sum of the frequencies is 20, and half of the difference is 2. Hence ω1 = 18 rad/s, and ω2 = 22 rad/s. In this script, 20 already represents half the sum of the frequencies, and 2 represents half the difference of the frequencies.
%DSB and AM
t=0:0.001:8;
y1=cos(2*t);
y2=cos(20*t);
y3=y1.*y2; DSB m(t) * cos(ωc t)
y4y4=y2.*(2+y1); AM (2+m(t)) * cos(ωc t)
bplot(2,2,1)
plot(t,y1)
subplot(2,2,2)
plot(t,y2)
subplot(2,2,3)
plot(t,y3)
subplot(2,2,4)
plot(t,y4)
Report your observations, based on the choices you made.
Build the amplifier shown in Figure 1.1.4, and design it with specifications as close as you can to the required ones: input is 1Vp sinewave at 1kHz, an offset of 5V, and a gain of 3. Use a single power supply set for 15V. Simulate it before you build it.
This part will be demonstrated in the lab by the instructor with different light-sensitive devices.
You do not have to build it.
Include all schematic and results. Compare simulated, measured, and calculated characteristics. Justify your choices with appropriate expressions. Make any comment or observation that you feel will enhance your understanding of the various circuits.
Frequency response of OpAmp-based active filters. Relation between bandwidth and gain. Slew rate. Design of first order and higher order active filters with OpAmps.
The 741 has a Gain-Bandwidth Product (GBP) of 1 MHz, and since the open loop gain is 200,000, hence the bandwidth is only 5Hz. With a constant GBP, if an amplifier is designed to have a gain of 10, then the bandwidth will increase to 100kHz (product=106). Various OpAmps have different specifications, and one chooses the device that would be suitable in any given design.
Slew rate is another specification that limits the ability of an amplifier to follow changes in the input from an amplitude point of view. Distortion can ensue from a varying high amplitude signal, regardless of its spectrum.
Design a first order lowpass and a highpass filters using an OpAmp and components available in your kit. Choose reasonable f-3dB frequencies, from tens of Hz to tens of kHz, so that you can test these circuits with the equipment on your bench. The highpass filter should have much lower f-3dB than the lowpass filter. Simulate the performance of the circuits (frequency response) with Multisim.
S. Franco "Design with Operational Amplifiers and Analog Integrated Circuits", McGraw-Hill 1988. Chapter 3, especially section 3.3.
Equipment needed from the stockroom: scope probe, resistance substitution box, leads.
Simulate only a non-inverting amplifier with a low gain, say 10. Check its frequency response. Op-amp performance is limited at high frequency; it behaves as a low-pass filter. Use the Bode plotter to evaluate its bandwidth, which is defined by f-3dB frequency.
Repeat the bandwidth measurements for a gain equal to 100. Repeat the procedure and compare the two gain bandwidth products.
NOTE: What happens to the phase shift between input and output signals at the f-3dB frequency?
Measure the slew rate of the non-inverting amplifier (gain of 10) by feeding a square wave at the input and compare it to the one specified by the manufacturer. You will get this parameter from the slope of the output waveform which will not change with increasing signal amplitude.
Build the low-pass filter of your design and check its frequency response. Drive the circuit with a sine wave and record input (constant) and output voltage for different frequencies. Be sure to obtain more points at the "interesting" part of the curve, near and well above f-3dB. Make preliminary graphs of the amplitude as a function of frequency in the laboratory; you will have a chance to discover early if something is wrong.
Measure also the phase shift between input and output signals. The goal is to see the phase shift as the frequency increases, passing through f-3dB. Make the measurements also at much lower and much higher frequencies than f-3dB. Measurement of phase shift is an accurate method of determining the filter characteristic frequency (f-3dB).
Build the high-pass filter of your design and test it only by finding the f-3dB frequency (check it through the amplitude and phase response). Build the circuit on the same board but using different components. If you have more than one op-amp in the same package, common power supply wiring will serve both circuits.
Connect the two circuits (high-pass and low-pass filters) in cascade to obtain a band pass filter. (Does it matter which is first?) Verify that it performs as a band-pass filter.
Alternatively, design and simulate a wide-band filter with a single op-amp, as shown in the figure below, with the same cutoff frequencies as the bandpass filter above. For this filter to work well, the low-pass frequency (low f-3dB) should be much lower than the high-pass (high f-3dB) frequency. Compare the two responses especially in the passband.
You are to design a Sallen-Key 6th order lowpass filter using Matlab, simulate your circuit using Multisim, and implement it for verification purposes. At the end of this process, you need to showcase your design in the lab to exhibit the relevant characteristics (3-dB cutoff frequency at 3.2kHz). You can use the closest values for resistors and capacitors in addition to 741 OpAmps. Observe if there are major deviations from the required specifications.
This is a 4th-order Sallen-Key lowpass filter
% CH4MP2.m : Chapter 4, MATLAB Program 2
% Script M-file computes Sallen-Key component values and magnitude
% responses for each of the five cascaded second-order filter sections.
omega_0 = 3000*2*pi; % Filter cut-off frequency
psi = [22.5 67.5]*pi/180; % Butterworth pole angles
f = linspace(0,6000,200); % Frequency range for magnitude response calculations
Hmag_SK = zeros(2,200); % Pre-allocate array for magnitude responses
for stage = 1:2,
Q = 1/(2*cos(psi(stage))); % Compute Q for current stage
% Compute and display filter components to the screen:
disp(['Stage ',num2str(stage),...
' (Q = ',num2str(Q),...
'): R1 = R2 = ',num2str(56000),...
', C1 = ',num2str(2*Q/(omega_0*56000)),...
', C2 = ',num2str(1/(2*Q*omega_0*56000))]);
B = omega_0^2; A = [1 omega_0/Q omega_0^2]; % Compute filter coefficients
Hmag_SK(stage,:) = abs(CH4MP1(B,A,2*pi*f)); % Compute magnitude response
end
plot(f,Hmag_SK,'r',f,prod(Hmag_SK),'b:')
xlabel('f [Hz]'); ylabel('Magnitude Response')
Stage 1 (Q = 0.5412): R1 = R2 = 56000, C1 = 1.0254e-09, C2 = 8.7524e-10
Stage 2 (Q = 1.3066): R1 = R2 = 56000, C1 = 2.4755e-09, C2 = 3.6254e-10
function [H] = CH4MP1(B,A,omega);
% CH4MP1.m : Chapter 4, MATLAB Program 1
% Function M-file computes frequency response for LTIC system
% INPUTS: B = vector of feedforward coefficients
% A = vector of feedback coefficients
% omega = vector of frequencies [rad/s].
% OUTPUTS: H = frequency response
H = polyval(B,j*omega)./polyval(A,j*omega);
This is a 10th-order Sallen-Key lowpass filter
% CH4MP2.m : Chapter 4, MATLAB Program 2
% Script M-file computes Sallen-Key component values and magnitude
% responses for each of the five cascaded second-order filter sections.
omega_0 = 3000*2*pi; % Filter cut-off frequency
psi = [9 27 45 63 81]*pi/180; % Butterworth pole angles
f = linspace(0,6000,200); % Frequency range for magnitude response calculations
Hmag_SK = zeros(5,200); % Pre-allocate array for magnitude responses
for stage = 1:5,
Q = 1/(2*cos(psi(stage))); % Compute Q for current stage
% Compute and display filter components to the screen:
disp(['Stage ',num2str(stage),...
' (Q = ',num2str(Q),...
'): R1 = R2 = ',num2str(56000),...
', C1 = ',num2str(2*Q/(omega_0*56000)),...
', C2 = ',num2str(1/(2*Q*omega_0*56000))]);
B = omega_0^2; A = [1 omega_0/Q omega_0^2]; % Compute filter coefficients
Hmag_SK(stage,:) = abs(CH4MP1(B,A,2*pi*f)); % Compute magnitude response
end
plot(f,Hmag_SK,'r',f,prod(Hmag_SK),'b:')
xlabel('f [Hz]'); ylabel('Magnitude Response')
Stage 1 (Q = 0.50623): R1 = R2 = 56000, C1 = 9.5916e-10, C2 = 9.3569e-10 Stage 2 (Q = 0.56116): R1 = R2 = 56000, C1 = 1.0632e-09, C2 = 8.441e-10 Stage 3 (Q = 0.70711): R1 = R2 = 56000, C1 = 1.3398e-09, C2 = 6.6988e-10 Stage 4 (Q = 1.1013): R1 = R2 = 56000, C1 = 2.0867e-09, C2 = 4.3009e-10 Stage 5 (Q = 3.1962): R1 = R2 = 56000, C1 = 6.0559e-09, C2 = 1.482e-10
Besides the usual circuit information, schematics, etc. attach tables with the data on frequency response measurements (amplitude and phase). The measured frequency distributions should be presented as discrete points and the Multisim simulations as continuous curves on the same graphs. This will allow for easy comparison of the data with simulation results. Use any software package to graph your plots. Discuss the agreement (or lack of it) between the measured and simulated functions, where needed.