1. Simulated Inductance
Experiment 25

2. Modification from Lab Manual
Write a MatLAB program
Determine the transfer function
Calculate the output voltage in phasor notation at the corner frequency.
obtain a Bode plot
Plot of AC Sweep in PSpice simulation
y-axis should be in dB
Frequency range from 1 kHz to 10 MHz
Construct a gyrator that has an effective inductance of 10mH.
Compare the operation of the gyrator with the 10mH inductor in an RL circuit where R = 2 kW.

3. Gyrator Inductors are far from ideal devices
Parasitic resistance because of the length of wire used to form the inductor.
Parasitic capacitance because of coupling between parallel loops of wire.

4. Integrated Circuits
Inductors are three dimensional devices, usually free standing
Very difficult to fabricate using standard semiconducting processes and to integrate in a silicon wafer.

5. Gyrator
Operational Amplifier circuit that has a frequency response similar to an inductor.

6. Low Pass RL Filter
At 0Hz, Vout = Vin. As the frequency increases and the inductor begins to act like an open, Vout approaches 0V.

7. Bode Plot of Resistor Voltage vs. Vin

8. High Pass RL Circuit
At 0Hz, Vout = 0V. As the frequency increases and the inductor begins to act like an open, Vout approaches Vin.

9. High Pass RL Filter

10. Voltage Transfer Function Plot: High Pass RL Filter

11. Bode Plot: High Pass RL Filter

12. Phase Plot: High Pass RL Filter

13. Low Frequency Response: As Expected

14. Higher Frequency Response: Limited by Op Amp

15. Information from 741 Datasheet
Operational Amplifiers are designed to have large open loop gain.
But, the frequency response of the circuit has been sacrificed to achieve this.

16. Temperature and Frequency Dependence of Open Loop Gain

17. Applications for Gyrator
Low frequency (f < 500 kHz) applications in:
Audio Engineering
Biomedical Engineering
Certain areas of power electronics

18. MatLAB

19. Defining a Vector
Three elements t=[0,.1,3] or t=[0 .1 3] t = Four Elements t=[0:3] t = Elements that include 0, then 0.1, and then increments of 1 until it reaches the largest number ≤ 3 t=[0,.1:3] t = Thirty one elements between 0 and 3 in increments of 0.1 t=[0:.1:3] t =

20. MatLAB
Suppose you have determined that the transfer function for your filter is:
You can put this transfer function into MatLAB
Define two vectors
A = [An, An-1, ….., A1, A0] where n, m ≥ 0 and
B = [Bm, Bm-1, ….., B1, B0] n does not have to equal m
H = tf(A,B)

21. Example High pass filter with a single-pole/single-zero
Let RC = 104 s/rad
A = [0, 10e3]
B = [1 10e3]
H = tf(A,B)
10000s
H = is returned when you run the program
10000s + 1

22. MatLAB: Bode Plots
Once you have entered the transfer function into MatLAB, you can use a predefined function ‘bode’ to automatically generate plots of the magnitude and phase vs. frequency.
Enter: bode(H)

24. Bode Plot Parameters

25. Complex Numbers
The default symbol for √-1 is i. However, MatLAB does recognize that j is equivalent to i.
The coefficient of the imaginary number must be placed before the ‘i’ or ‘j’.
If you typed c = 2-3j, MatLAB interprets it as
c = i
To find components of complex number
real(c) returns 2
imag(c) returns -3

26. Magnitude and Phase Magnitude of a complex number
Is the square root of the square of the real component plus the square of the imaginary component
Phase of a complex number
Is the arc tangent of the imaginary component divided by the real component
Must change to degrees if the output of the arc tangent is given in radians