ELE 343 Electronics II
Improved 2N3904 SPICE Model


Figure 1.   Simulation using the old model 

       Q2N3904
               NPN
          IS    6.734000E-15
          BF  416.4
          NF    1
         VAF   74.03
         IKF     .06678
         ISE    6.734000E-15
          NE    1.259
          BR     .7371
          NR    1
          RB   10
          RC    1
Old SPICE Model Parameters


Figure 2.   Simulation using the new model

Calculated currents do not agree well with simulations for the Lab 2 circuit shown in Figure 1. This is due to errors in the SPICE model parameters for the 2N3904 transistor.

Calculated Currents

The calculated collector current Ic,

Ic = (VCC - Vbe)/(Rb/ß - Re)

Ic = (10-0.7)/(820/200 - .22) = 2.15mA

As can be seen in Figure 1, the simulated collector current is 1.638mA. The beta in the SPICE model is 416.4. If this higher beta is used in the calculation, Ic becomes 4.25mA. Using the simulated Vbe of 0.677V rather than 0.7V does not bring the calculation and the simulation into agreement.

SPICE Calculations

Neglecting the Early effect, SPICE calculates the collector current using an equation approximately equal to

Ic = IS*exp(Vbe/(NF*Vt))
where in this simulation Vbe = 0.677V. Vt = 0.0259V at T=300 degrees K. Plugging in these values and the SPICE parameters IS and NF shown on the right results is an Ic of,
Ic = 1.51mA
This agrees with the simulated result of 1.64mA.

SPICE Base Current

The formula SPICE uses to calculate base current is

Ib = Ic/BF + ISE*exp(Vbe/(NE*Vt))
The second term accounts for leakage currents important at low Vbe. These leakage currents do not contribute to Ic. The theoretical NE is 2. This makes the exponential small. ISE is usually larger than IS. The second term dominates at low Vbe but not in the normal operating region. The SPICE parameters used in the simulation result in a value for these leakage currents that is too large.

New Model

In Lab 1 model parameters for the 2N3904 transistor were determined.

BF = 200
IS = 2E-15
NF = 0.95
Editing the 2N3904 model to use these values and also letting NE = 2 results in good agreement between hand calculations and simulations. Figure 2 is the result of resimulating the circuit using the new model. The simulated Ic is 2.20mA. This is in good agreement with the calculated value of 2.15mA. NE = 2 greatly reduces the leakage current by reducing the exponent in the formula.

More information is available in the simulation output file.