RLC-calculator for a PCB trace

This article contains MATLAB script for the calculation of the parasitic parameters of the PCB trace.

Script limitations:

• Valid under 1GHz
• Skin effect is omitted
• Copper roughness is omitted
• Loss tangent is omitted
• Geometry limitations:
• W/H < 7.475 - 1.25*(T/H) - for a microstrip
• W/B < 2.375 - 1.25*(T/B) - for a stripline

First coefficient in equation - conversion from inches to m.

H - height

W - width

Microstrip Equations:

$$R = 1000 \frac{\rho_0(1 + \alpha (temp-25))}{TW} [m\Omega/m]$$ $$C = 26.378 \frac{ (\epsilon_r + 1.41)}{\ln{ \frac{5.98H}{0.8W + T} } } [pF/m]$$ $$L = 199.65 \ln \frac{ 5.98 H} {0.8W + T} [nH/m]$$ $$Z = 87 \frac{\ln{\frac{5.98 H}{0.8W+ T}} }{ \sqrt{\epsilon_r + 1.41}}$$

Stripline Equations:

$$R = 1000 \frac{\rho_0(1 + \alpha (temp-25))}{TW} [m\Omega/m]$$ $$C = 39.37 \frac{ \epsilon_r \sqrt{2} }{\ln{ \frac{1.9 B}{0.8W + T} } } [pF/m]$$ $$L = 199.8425 \ln \frac{ 1.9 B} {0.8W + T} [nH/m]$$ $$Z = 60 \frac{\ln{\frac{1.9 B}{0.8W+ T}} }{ \sqrt{\epsilon_r}}$$

1   
2%% PCB lumped parameters calculator (microstrip/stripline)
3% Author: A.Sidun
4% Source: AnalogHub.ie
5% Limitations:
6% - Valid under 1GHz
7% - Skin effect is omitted
8% - Copper roughness is omitted
9% - Loss tangent is omitted
10% - Geometry limitations:
11% W/H < 7.475 - 1.25*(T/H) -  for a microstrip
12% W/B < 2.375 - 1.25*(T/B) - for a stripline
13% Source: https://resources.system-analysis.cadence.com/blog/msa2021-is-there-a-pcb-trace-inductance-rule-of-thumb
14
15%% Input parameters
16type = "microstrip";				% can be microstrip or stripline
17temp = 25;					% temperature [C]
18length = 1e-3;					% trace length [m]
19width = 0.5e-3;                                 % trace width [m]
20thickness = 35e-6;				% trace thickness [m]
21height = 0.4e-3;				% height over a plane [m] 
22
23%% Constants
24ro = 1.724e-8;					% resistivity of copper [Ohm/m]
25alpha = 3.9e-3;					% temperature coefficient of copper
26eps_r = 4.46;					% relative permittivity of copper
27
28%% Calculations
29B = 2*height+thickness;				% plane-to-plane distance [m]
30switch type
31    case "microstrip"
32        if ( width/height < 7.475 - 1.25*(thickness/height) )
33            R_lumped = 1e3*ro*(1 + alpha*(temp-25))/(thickness*width);				% mOhms/meter
34            C_lumped = 26.378*(eps_r+1.41)/( log( 5.98*height/(0.8*width+thickness) ) );	% pF/meter
35            L_lumped = 199.65*log( 5.98*height/(0.8*width + thickness) );			% nH/meter
36            Z = 87*log(5.98*height/(0.8*width + thickness)) / sqrt(eps_r + 1.41);
37            
38            R = R_lumped*length; % mOhm
39            L = L_lumped*length; % nH
40            C = C_lumped*length; % pF
41            
42            disp("PCB " + type + " parameters:")
43            disp("R = " + R + " mOhms")
44            disp("C = " + C + " pF")
45            disp("L = " + L + " nH")
46            disp("Z = " + Z + " Ohm")
47        else 
48          disp("Please check geometry of the trace.")  
49        end
50     case "stripline"
51        if ( width/B < 2.375 - 1.25*(thickness/B) )
52           R_lumped = 1e3*ro*(1 + alpha*(temp-25))/(thickness*width);                   % mOhms/meter
53           C_lumped = 39.37*eps_r*sqrt(2) / ( log(1.9*B/(0.8*width + thickness)) );     % pF/meter
54           L_lumped = 199.8425*log( 1.9*B/(0.8*width + thickness) );                    % nH/meter
55           Z = 60*log(1.9*B/(0.8*width + thickness)) / sqrt(eps_r); 
56           
57           R = R_lumped*length; % mOhm
58           L = L_lumped*length; % nH
59           C = C_lumped*length; % pF
60           
61           disp("PCB " + type + " parameters:")
62           disp("R = " + R + " mOhms")
63           disp("C = " + C + " pF")
64           disp("L = " + L + " nH")
65           disp("Z = " + Z + " Ohm")
66         else 
67          disp("Please check geometry of the trace.")  
68        end
69end