tf2zp how to use k value

Setup:

2_a Coef and pole/zero pairs and gain (k)

aN = 2.11e-12;

bN = 3.90e-6;

cN = 0;

aD = 1.07e-10;

bD = 2.97e-5;

cD = 1;

num =[aN bN cN];

den =[aD bD cD];

[z,p,k] = tf2zp(num,den)

z =

1.0e+06 *

0

-1.8483

p =

1.0e+05 *

-2.3836

-0.3921

k =

0.0197

ZA = .0197*( s*(1 + s/1848300) / ((1 + s/238360)*(1 + s/39210)));

Ran the following:

R1 = 3000;

R2 = 16000;

R4 = 360;

C2 = 1.3e-9;

C4 = 1.5e-9;

w1 = (1/(C4*R4));

f1 = w1/2*pi;

w2 = (1/(C4*(R4+R1)));

f2 = w2/2*pi;

w3 = (1/(C2*R2));

f3 = w3/2*pi;

s = tf('s');

Z1 = R1*( (1 + s/w1)/(1 + s/w2) );

Z2 = R2*(1 + w3/s);

Z = minreal(Z1/(Z1 + Z2));

ZA = (.0197)*( s*(1 + s/1848300) / ((1 + s/238360)*(1 + s/39210)));

fmin = 10; % minimum frequency = 10 Hz

fmax = 10e6; % maximum frequency = 10 MHz

% Set Bode plot options

BodeOptions = bodeoptions;

BodeOptions.FreqUnits = 'Hz'; % we prefer Hz, not rad/s

BodeOptions.Xlim = [fmin fmax]; % frequency-axis limits

BodeOptions.Ylim = {[-200,200];[-360,360]}; % magnitude and phase axes limits

BodeOptions.Grid = 'on'; % include grid

figure(2);

% define plot title

BodeOptions.Title.String = 'Z1/(Z1+Z2) vs ZA';

bode(Z, BodeOptions, 'b', ZA, BodeOptions, 'r'); % generate the magnitude and phase responses

legend('Z1/(Z1+Z2)', 'ZA')

And my gain from ZA does not match Z1/(Z1 + Z2).

If I modify to this:

ZA = 20log(.0197)*( s*(1 + s/1848300) / ((1 + s/238360)*(1 + s/39210)));

then ZA phase is mesed up.

How does one deal with k?

Answer 1

[KALYAN ACHARJYA]

tf2zp how to use k value

When the code exucate the following line

[z,p,k] = tf2zp(num,den);

here k represents the gain of the transfer functuion. The k value avalible in current variable list (workspace), just use the variable k in your code when it required after the tf2zp line.

[CD]

So I took the results from tf2zp:

ZA = .0197*( s*(1 + s/1851900) / ((1 + s/238970)*(1 + s/39130)));

and fed it into the bode function and the phase is perfect and the shape of the magnitude is perfect though the gain of the magnitude is off.

Trying to figure out where the problem is.