Complex variable substitution using Symbolic Toolbox no working as expected.

For the code:

% Define symbolic variables
syms R81 R79 R80 C37 C67 T z fs complex
syms w s complex

% Define the frequency-domain transfer function
h_w = -1 / ((R81 - 1i/(C37*w)) * (1/(R79 + R80) + C67*w*1i));

disp('Frequency-domain transfer function (h(w)):');

Frequency-domain transfer function (h(w)):

disp(char(h_w));

-1/((R81 - 1i/(C37*w))*(C67*w*1i + 1/(R79 + R80)))

% Substitute s = j*w into Laplace domain
s = 1i*w; % Substitute s = j*w
h_s = simplify(subs(h_w, w*1i, s));

disp('Laplace-domain transfer function (H(s)):');

Laplace-domain transfer function (H(s)):

disp(char(h_s));

-1/((R81 - 1i/(C37*w))*(C67*w*1i + 1/(R79 + R80)))

-----------

The output is the identical equation: h_w = h_s = -1/((R81 - 1i/(C37*w))*(1/(R79 + R80) + C67*w*1i)) where h_s should be h_s = - (s * C37 * (R79 + R80)) / ((R81 * s * C37 - 1) * (1 + s * C67 * (R79 + R80)));

I'm using Symbolic Math Toolbox, Version 8.5, (R2020a). Has anyone else seen this and / or what am I doing wrong?

[Walter Roberson]

syms R81 R79 R80 C37 C67 T z fs complex

Note that there is no flag named complex for syms . What you have done there is to declare a symbolic variable named complex . All symbolic variables default to complex unless specifically restricted to real or positive or assume() or assumeAlso() are used.

Answer 1

[Paul]

% Define symbolic variables
syms R81 R79 R80 C37 C67 T z fs %complex
syms w s % complex
% Define the frequency-domain transfer function
h_w = -1 / ((R81 - 1i/(C37*w)) * (1/(R79 + R80) + C67*w*1i)),pretty(h_w)

                      1
- ----------------------------------------
  /         1i  \ /     1                \
  | R81 - ----- | | --------- + C67 w 1i |
  \       C37 w / \ R79 + R80            /

% s = 1i*w -> w = s/1i
h_s = subs(h_w,w,s/1i),pretty(h_s)

                    1
- -------------------------------------
  /         1   \ /             1     \
  | R81 + ----- | | C67 s + --------- |
  \       C37 s / \         R79 + R80 /

Answer 2

[Walter Roberson]

s = 1i*w; % Substitute s = j*w
h_s = simplify(subs(h_w, w*1i, s));

You are asking to substitute 1i*w for w*1i . However, expressions are automatically rewritten to internal order before proceeding, so you are effectively asking to substitute w*1i for w*1i . Which of course does nothing useful.