The above figure represents a two stage circuit. Recall, the transfer function relates. Vout

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1 LABORATORY 12: Bode plots/second Order Filters Material covered: Multistage circuits Bode plots Design problem Overview Notes: Two stage circuits: Vin1 H1(s) Vout1 Vin2 H2(s) Vout2 The above figure represents a two stage circuit. Recall, the transfer function relates Vout ( s) the ratio the input to the output of a stage, = H ( s). In the above figure, Vin ( s) recognize that V out1 = V in2. The transfer function can be applied to each stage. Applying the transfer function to each stage we can derive the equation, Vout 2 ( s) = H 2 ( s) Vin2 ( s) = H 2 ( s) Vout1( s) = H 2 ( s) H1( s) Vin 1( s). Finally, the relationship Vout 2 ( s) between V out2 and V in1 can be written as = H 2 ( s) H1( s). This equation is the Vin 1( s) product of the two transfer functions. By designing each stage to produce a particular circuit response, the final output can be designed to meet a specific goal.

2 Filter types: Lowpass filter Highpass Filter

3 Bandpass Filter Notch/Bandstop Filter

4 Measuring Phase in PSpice: Under the PSpice tab, 1. Click Markers 2. Click Advanced 3. Choose Phase of Voltage 4. You will now have a marker you can place on the circuit to measure phase in degrees. 5. Important qualification regarding this marker in the following text. PSpice has a phase marker that can be used like the voltage markers. However, it is the phase at a node relative to ground rather than the phase across a component. Therefore, in order to determine the phase across a component, one of the component legs must be connected to ground. Recall, the order of components in series does not matter and won t affect the circuit response. Measuring db in PSpice: Under the PSpice tab, 1. Click Markers 2. Click Advanced 3. Choose db Magnitude of Voltage 4. You will now have a marker you can place on the circuit to measure phase in degrees. 5. Important qualification regarding this marker in the following text. As with phase, the db is determined at the node relative to ground. One additional aspect is that this calculation is the db value of the voltage, 2log( Vout(jω) ), not the transfer function. To obtain a plot of the transfer function, recognize that Vout( jω) 2log( H ( jω) ) = 2log = 2log( Vout( jω) ) 2logVin( jω) Vin( jω) Since Vin is typically the source and a constant, than the PSpice db plot can be shifted vertically by a fixed value. However, if you set the source amplitude to 1V, the log expression for the source term evaluates to zero and the db expression for the voltage is then equivalent to the db expression for the transfer function.

5 Laboratory: Part 1: R1 1k Vin U1 R4 OUT 1k C1 OPAMP 1E6 R3 ~9k C2 1E6 R2 1k Vout Determine the transfer function for the voltage across the capacitor, C2 H(s) = (symbolically) This circuit is which of the following? highpass filter, lowpass filter, bandpass filter, notch filter What are the zeros of the transfer function? What are the poles of the transfer function? What is the gain of the passband, in db? What is the slope of the stopband in db/decade?

6 Build the circuit and measure the output voltage for various frequencies. Your source amplitude should 2mV. Your Oscilloscope V/div should be.5v/div or less. Fill in the following table with your calculations and Mobile Studio measurements. Remember to scale your measured output voltage with your input voltage to obtain the transfer function. Reminder: The amplifier requires 9/9 voltage connections. You should double check your batteries and make sure they still have close to a 9V supply. Sometimes, storing them in the kits without a cover results in a short circuit connection across the leads, which discharges the battery. Magnitude, H(s) Frequency [Hz] Calculated Measured 2log H(s) (use measured value) Using your measured results, generate a Bode plot of the magnitude. Compare the measured results to your analytic expression and a PSpice simulation.

7 Part 2: Vin1 R1 1 C1 1E6 U2 OUT OPAMP R3 C2 1E6 R4 1k Vout R2 1k ~9k Determine the transfer function for the voltage across the resistor, R4. H(s) = (symbolically) This circuit is which of the following? highpass filter, lowpass filter, bandpass filter, notch filter What are the zeros of the transfer function? What are the poles of the transfer function? What is the gain of the passband, in db? What is the slope of the stopband(s) in db/decade?

8 Build the circuit and measure the output voltage for various frequencies. Your source amplitude should 2mV. Your Oscilloscope V/div should be.5v/div or less. Fill in the following table with your calculations and Mobile Studio measurements. Remember to scale your measured output voltage with your input voltage to obtain the transfer function. Magnitude, H(s) Frequency [Hz] Calculated Measured 2log H(s) (use measured value) Using your measured results, generate a Bode plot of the magnitude. Compare the measured results to your analytic expression and PSpice simulation.

9 Design a lowpass filter that meets the following specifications. 1. Cutoff frequency: 1.59kHz 2. 6dB rolloff in the stopband 3. A single unity gain opamp 4. H(jω) 3dB relative to the passband at the cutoff frequency. (Remember a triple pole has a 9dB correction relative to the straight line approximation. You will need to underdamp a second order circuit.) 5. Use L and C component values found in your kit. You can use resistors found on the center table in the laboratory room. Some flexibility exists in meeting the specifications. In design problems, perfection is not usually possible, but deviations should be small. If you don t quite meet specification, explain why and explain what you would do to fix the problem. Laboratory: Part 1: Determine the transfer function that meets the above specifications H(s) = (symbolically) Draw the circuit, labeling the component values

10 Build the circuit and verify that the specifications are met by taking measurements at appropriate frequencies. You should base your Vin amplitude around that setting. Magnitude, H(s) Radial Frequency [rad/s] Calculated Measured Vout / Vin 2log H(s) (use measured value) 1 3 1E3 3E3 9E3 1E3 15E3 2E3 3E3 1E3 Due to the steep rolloff and noise effects, you may have difficulty obtaining data as you move further into the stopband. For the same circuit, perform an AC Sweep in PSpice and compare your results.