ECEN Network Analysis Section 3. Laboratory Manual

Transcription

1 ECEN Network Analysis Section 3 Laboratory Manual LAB 07: Active Low Pass Filter Oklahoma State University School of Electrical and Computer Engineering. Section 3 Laboratory manual Spring 2016

2 1. Objective The objective of this lab section is to examine the frequency-response of a 1 st -order low pass filter, and to assess the load dependence of the built low-pass filter. 2. Introduction In the previous lab you measured the steady-state output of a first-order circuit to a sinusoidal input at several frequencies. So you have already learned about the frequency-dependent response of a first-order circuit. What you examined in that lab is a passive filter, and in this lab, you are going to examine an active filter, which is advantageous compared to its passive counterpart in terms of load-independence, and the flexibility of setting a gain higher than 1. An active filter is built by active components, most often an operational amplifier. An idea op-amp should have infinite bandwidth; however, the op-amps you have in your kit usually have a bandwidth up to 1MHz. So besides the design that you have for the filter band-width parameters, the bandwidth of the op-amp will also affect the overall bandwidth of the filter, specifically for a high-pass filter. The Unity Gain Buffer Amplifier Figure 1 What does the circuit do? The circuit essentially just makes Vout=-Vin for an idea op-amp. This circuit provides a buffer between Vin and Vout such that a change in the load connecting to Vout does not change Vin-----very important in circuit application, specifically in signal conditioning (such as filtering). Placing an op-amp on a bread-board Here is a drawing (only illustrative, actual pin definition should refer to the manual of the op-amp) of what the circuit should look like on a circuit board. Figure 2 Important procedures to connect an op amp (for LM741, check pins for other chips): Put the integrated circuit chip into your circuit board. Be sure to straddle the center "groove" so that you do not short pins together. Set the power supply based on the op-amp specifications (uni-polar, or bi-polar, mostly 12~15Volts) before connecting to the op-amp circuit. TURN OFF the power supply. For LAM741, it will use bi-polar power supply. Connect the positive supply to pin #7, and the negative supply to pin #4. Color-code the power-wires: you can have your own choice of colors, however, often red is for positive, green or white is for GND, yellow is for negative and other colors for inputting or outputting signals. Laboratory manual Spring 2016

3 Connect the circuit shown above in figure 2. The output is pin #6. o The inverting input (with the minus sign) is pin #2. Connect the operational amplifier output from pin #6 to here. o The non-inverting input (with the plus sign) is pin #3. Connect the output of the filter (the voltage from the capacitor in the filter circuit) to this pin. o Connect the output of the inverting amplifier circuit to the oscilloscope. o Be sure that the ground from the filter circuit is connected to the ground on the oscilloscope and the common on the power supply. When you have all of the wiring above completed, then you can turn on the signal source and turn on the power supplies (+12 and -12v as indicated above). Figure 3 Low Pass Active Filter The simplest active filter is the Low Pass Filter as shown in Figure 3. It can be considered as a passive filter with gain-control by op-am. Its transfer function (and thereby the frequency response) is exactly the same as that for the previously seen RC low pass filter with infinite load resistance, the only difference being it uses an op-amp as a buffer which maintains the same cut-off frequency even though the load may change. The cut-off frequency (where the gain becomes of the pass-band or the maximum gain) of the low-pass filter shown in Fig. 3 is 1 st -order active low pass filer with gain higher than 1. The active low-pass filter shown in Fig. 4 consists of an RC network connected to a non-inverting amplifier. The DC voltage gain of this circuit can be shown to be (1 + R2/R1); therefore a different pass-band gain can be set by changing the values of R1 and R2. The pass-band gain is typically described by db value. The conversion formula is Gain in Decibel=20 log (Vout/Vin). So 10 times is 20dB, 100 times is 40dB, 0.1 times is -20dB. Figure 4 Using the formulae above and your understanding of opamp filters, design a non-inverting active low pass filter circuit, similar to the one in Fig. 4, that has a DC voltage gain of 10, a cut-off frequency close to 320 Hz Laboratory manual Spring 2016

4 (within + 10%, subject to R and C availability) and a high frequency input impedance (value of resistor R) of 5KΩ. 3. PRE-LABORATORY ASSIGNMENT The pre-lab section helps you to understand the requirements of the lab. The pre-lab assignment MUST be completed before you perform the hands-on laboratory measurement. The pre-lab worth 40% of lab-8 grade. 3.1 Pre-Lab Assignments: Use the circuit configuration shown in Fig. 4, but you will use R = 5KΩ. Derive the voltage transfer function H(jω) and show that your design meets the three specifications above % pts Use PSpice to find the frequency-response ( (t) versus the frequency of input) of this circuit, using a sinusoidal input of 500mV amplitude and a frequency ranging from KHz. Show both the amplitude and phase responses. The amplitude response is the amplitude of output/input versus the input frequency, and the phase response is the phase-shift of the output with respect to the input versus the input frequency. Check that cutoff frequency, where the gain is of the maximum gain, is the predicted value %pts Filter under load: Connect a load resistor of 1kΩ and 6.8 KΩ, respectively, across the outputs of your active filter (between Vout and GND). Use Pspice to find the frequency-responses (amplitude response only) when each load is connected, as you did in (you should see no change in the response) %pts Disconnect the op-amp, and connect the 1kΩ or 6.8 KΩ resistor loads directly to the RC low-pass filter (that is between GND and the terminal of R previously connecting to the + of op-amp). Use PSpice to find the frequency-response (amplitude response only) when the 1kΩ resistor is connected and the 6.8 KΩ resistor is connected, respectively (which means you will measure the voltage across this load-resistor). (you should see the difference now) %pts You will need a flash drive to save the data from the oscilloscope. Check the data saved in your drivesk before leaving lab as no credit can be given for lost data. Find the pin-definition of the Op-amp that you are going to use. out 4. LABORATORY ASSIGNMENT 4.1 Activities: Construct the circuit designed in You will use a 500mV-amplitude (so 1.0V peak-to-peak) sinusoidal signal of different frequencies to measure the frequency response of the circuit you just built. You can use either the oscilloscope or the Gain- Phase meter to find the amplitude and phase response of the circuit at the given frequency. Measure the amplitude and phase responses at the following frequencies: 100Hz, 250Hz, 500Hz, 1KHz, 2.5KHz, 5KHz, 10KHz, 25KHz, 50KHz, and the cut-off frequency that you have calculated in You are going to plot the measured amplitude and phase responses in your lab report using a logarithmic frequency scale as the x_axis. (for y_axis, you need to decide using log-scale or linear-scale) Verify experimentally (you do not have to take record of the frequency responses as you did in 4.1.2, but you must test that the load does not noticeably affect the frequency response) Remove the op-amp. As you did in 3.3.4, connect the load resistor to the RC low-pass filter directly. Measure the amplitude response when each of the load resistors is connected, at the 10 frequencies suggested in (Note: now the pass-band gain would be 1, instead of 10, so you will see a much smaller output signal. At your judgment, you could increase the amplitude of input signal if that gives you better measurements, but be aware that the amplitude response is output_amplitude/input_amplitude.) 4.2 Laboratory Report: Cover page % The cover page should include (1) the course name, lab-sections, dates, lab numbers, etc. that indicate the comprehensive lab information, (2) the names of the group members, and the signatures of the members. The lab should be the work of the lab-group only, no discussion with other group members is allowed. Laboratory manual Spring 2016

5 4.3.2 Objective of the lab: % Describe the objective of this laboratory section with your own words Completed pre-lab (with the signature of TA): % Results and data analysis % Based on the order of the laboratory activities defined in 4.1, organize the estimated and observed responses of the circuits. This section shall include the following components for each experimental set up of and The amplitude response measured from and plotted by MATLAB % The phase response measured from and plotted by MATLAB % Based on the measurements 4.1.4, plot the three sets of amplitude-response data (no load, 1KΩ load, 6.8KΩ load) in one figure to demonstrate the load-dependence of a passive filter % Discussions and conclusion: % What are the similarities and differences of active and passive low pass filter circuits? For a passive low-pass filter, if the load resistance becomes lower, will the cut-off frequency with the load become smaller? Use relevant equations to support your conclusions if necessary. Laboratory manual Spring 2016