Equivalent Circuit

This page presents a typical large signal model of a p-n junction diode [1] that is similar to that found in circuit simulators such as SPICE. The model is comprised of a voltage controlled current source (\(i_D\)), a series resistance (\(R_D\)) and two nonlinear capacitors (\(C_T\) and \(C_J\)). The diode equivalant circuit is shown in the figure below.

Smiley face
Equivalent circuit used to model a p-n diode.

Large Signal Model

The VCCS \(i_D\) is modelled by a nonlinear function of the applied p-n junction voltage \(v_D\) that is divided into four distinct operating regions:

$$ i_D(v_D) = \left\{ \begin{array}{l l l l} I_S\left(e^\frac{v_D}{nv_T}-1\right) + v_DG_{min} & v_D \geq -5v_T \\ -I_S + v_DG_{min} & -BV \lt v_D \lt -5v_T \\ -I_{BV} & v_D = -BV \\ -I_S\left(e^{-\frac{BV+v_D}{nv_T}}-1 + \frac{BV}{v_T}\right) & v_D \lt -BV \\ \end{array} \right. $$ $$ v_T = \frac{kT}{q} \\ $$

Charge storage effects are modelled by two nonlinear capacitances that are also functions of the applied p-n junction voltage \(v_D\):

$$ C_J(v_D) = \left\{ \begin{array}{l l} \frac{C_{J0}}{\left(1-\frac{v_D}{v_J}\right)^m} & v_D \leq v_JFC \\ F_1C_{JO} + \frac{C_{J0}}{F_2}\left(F_3 + \frac{mv_D}{v_J}\right) & v_D \gt v_JFC\\ \end{array} \right. $$ $$ C_T(v_D) = \frac{qi_D(v_D)\tau\tau}{nkT} \\ $$

where \(F_1\), \(F_2\) and \(F_3\) are constants whose values are:

$$ F_1 = \frac{v_J}{1-m} \left(1 - \left(1-FC\right)^{1-m}\right) \\ $$ $$ F_2 = \left(1-FC\right)^{1-m} \\ $$ $$ F_3 = 1 - FC(1+m) \\ $$

The table below lists the p-n junction diode model parameters.

Parameter Descripton Units
\(I_S\) Saturation current A
\(n\) Emission current
\(BV\) Reverse breakdown "knee" voltage V
\(I_{BV}\) Reverse breakdown "knee" current A
\(R_S\) Parasitic resistance \(\Omega\)
\(C_{J0}\) Zero bias p-n capacitance coefficient F
\(v_J\) p-n potential V
\(\tau\tau\) Transit time s
\(m\) p-n grading coefficient
\(G_{min}\) Minimum conductance \(\Omega^{-1}\)
\(k\) Boltzmann constant \(1.3806503\times10^{-23}\) \(m^{2}kgs^{-2}K^{-1} \)
\(T\) Temperature K
\(q\) Electron charge magnitude \(1.60217646\times10^{-19}\) C

Octave Code

	  function F = diode(Vd, Is, N, BV, Ibv, Gmin, Cjo, Vj, m, tt, FC, Rs, temp)
	  F = zeros(4,1);    % a column vector
	  
	  I=0;
	  
	  q = 1.60217646e-19;
	  k = 1.3806503e-23;
	  T = 273.15 + temp;
	  Vt = k*T/q;
	  
	  if(Vd >= -5*Vt)
	  I = Is*(exp(Vd/(N*Vt)) - 1) + Vd*Gmin;
	  elseif ((Vd > -BV) && (Vd < -5*Vt))
	    I = -Is + Vd*Gmin;
	  elseif(Vd == -1*BV)
	    I = -Ibv;
	  elseif(Vd <= -BV)
	    I = -Is*( exp(-1*(BV + Vd)/(N*Vt)) -1 + BV/Vt);
          endif

	  if(Vd < FC * Vj)
	    Cj = Cjo/(1 - (Vd/Vj))^m;
	  else
	    F1 = (Vj/(1-m))*(1-(1-FC)^(1-m)); 
	    F2 = (1 - FC)^(1+m);
	    F3 = 1 - FC*(1 + m);
	    Cj = Cjo*F1 + (Cjo/F2)*(F3 + (m*Vd/Vj));
	  end

	  Ct = q*I*tt/(N*k*T);
	  C = Cj + Ct;
	  
	  F = [Rs;Cj;Ct;I];
	

References

1. Giuseppe Massobrio & Paolo Antognetti (1993). Semiconductor Device Modeling with SPICE. 2nd ed. New York: McGraw-Hill. p1-43.