Symbolic Analysis by Computer finds Transfer Function

Symbolic Analysis produces a transfer function of a circuit in terms of its L’s, C’s, R’s, and amplifiers. Given the circuit in the post header, we might want to write a transfer function without going through a detailed nodal analysis, by hand, to arrive at it.

There are several programs that can obtain the transfer function from the topology, including

XFUNC – A Dos program but works very well.

TOPCAP – by J. B. Grimbleby    6 December 1997, Department of Engineering, University of Reading

ElecFilDes – Uses TOPCAP by permission but allows the topology to be described by a PSPICE file.

ElecFilDes was used to provide all the graphics and equations in this post. We can have a PSPICE file in which all the element values are set to 1, as a placeholder, because symbolic analysis only defines the transfer function in terms of L’s, C’s, R’s, and amplifier.

Such a PSPICE file would look like

* ACTIVE LOWPASS  BUTTERWORTH ORDER= 3

.WIDTH OUT=80

.AC LIN  1000  0  0

VIN 1 0 AC 1

R1 1  2  1

R2 2  3  1

R3 3  4  1

C1 2  0  1

R4 2  0  1

C2 3  5  1

C3 4  0  1

EAMP1 5  0  4  5  1000000

.PRINT AC VM( 5 )

.PROBE VM( 5 )

.END

Processing this file with ElecFilDes ( www.elecfildes.com ), the symbolic analysis becomes

Numerator:

+ s^0

Number of terms = 1

Denominator:

+ s^0

+ R3 * C3 * s^1

+ R2 * C3 * s^1

+ R2 * R3 * C2 * C3 * s^2

+ R1 * C1 * s^1

+ R1 * C3 * s^1

+ R1 * R3 * C1 * C3 * s^2

+ R1 * R3 * C2 * C3 * s^2

+ R1 * R2 * C1 * C3 * s^2

+ R1 * R2 * R3 * C1 * C2 * C3 * s^3

Number of terms = 10

Checking the symbolic analysis with the design equations (given by ElecFilDes), it can be seen that they agree.