# Application Gallery

 Small-signal Analysis

In this part of the example we will look at the small-signal behavior of the pn-junction diode under different frequencies of operation.  The project file ac_pn_diode.ldev provide at the top level page can be used to perform the small signal ac analysis.  Alternatively, the instructions at the bottom of the Modeling Instructions page can be used to modify the existing project file.  In the small-signal analysis, a small signal ac voltage is applied on top of the dc (steady-state) bias and the small-signal currents and voltages at the contacts are reported.  The solver region also reports the small signal charge and electric field profiles.

## Reverse Bias

In reverse bias, the depletion region of the diode becomes larger and the potential barrier increases.  The capacitance at the p-n junction (junction capacitance) makes the diode behave like a capacitor.  The equivalent circuit of the diode can be expressed as a simple capacitor whose value is equal to the junction capacitance.  In the "Results and Discussion" page, we have calculated the value of this capacitance using the steady-state solver.  In this section, we will use the small-signal solver mode to calculate the junction capacitance in a much simplified manner.  We will also look at the effect of frequency on the junction capacitance.

Open the ac_pn_diode_Cj.lsf script file in CHARGE and run it.  The file will load and run the ac_pn_diode.ldev project file.  Once the simulation is run, the script will read the small-signal ac current at the "emitter" contact which is also the input contact where the small signal voltage was applied.  It will then calculate the admittance of the diode using Y = dI/dV = i/v where i and v are the small signal ac current and voltage at the emitter contact, respectively.  The real part of the admittance if the small conductance of the diode and can be neglected at reverse bias.  The imaginary part of the admittance if due to the junction capacitance and is equal to j*w*Cj, where j is the imaginary unit, w is the angular frequency, and Cj is the junction capacitance.  The script will plot the junction capacitance at different bias voltages under low frequency of operation (1 kHz) along with the analytic junction capacitance as shown in the figure below (left).  The figure on the right (also generated by the script) plots the junction capacitance under a reverse bias voltage of 2 V (-2 V at emitter) as a function of frequency.  It can be seen that at extremely high frequency of operation (> 1 GHz), the junction capacitance starts to deviate from the steady-state (low-frequency) value.

 Junction capacitance of pn-junction diode under reverse bias pn diode junction capaciatnce as a function of frequency

## Forward Bias

The junction capacitance dominates the capacitance of a pn-junction diode in reverse bias.  In forward bias however, the charge storage capacitance or the diffusion capacitance becomes dominant.  The small-signal conductance of the diode also becomes large in forward bias as the diode turns on.  The equivalent circuit of the diode in forward bias thus becomes a parallel combination of the conductance and the diffusion capacitance.  The value of this conductance and capacitance can be again be calculated by performing a small-signal analysis.

To perform the small-signal analysis in forward bias, we will need to update the applied bias voltage in the emitter contact.  Switch back to the "Layout" mode and apply a bias voltage of 0 to 0.5 V at the emitter contact in 6 steps (step size of 0.1 V).  Run the simulation and use the script file ac_pn_diode_forward.lsf to plot the conductance and diffusion capacitance as a function of frequency (shown below).  The plot shows that the diffusion capacitance unlike the junction capacitance decreases rapidly at moderately high frequency of operation (≥ 100 kHz).

Forward bias conductance and capacitance versus frequency

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