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In this part of the example, we will perform small signal analysis on the MOSFET under investigation.  We will calculate the input and output impedance of the MOSFET as a function of frequency and we will evaluate the bandwidth of the device by calculating the unity-current-gain cutoff frequency (fT).  From the simulation results we will calculate parameter values for the small-signal equivalent circuit of the MOSFET.

 

A simplified version of the small-signal equivalent circuit of the MOSFET is shown below.  Here Cgs and Cgd are the gate-source and gate-drain capacitance.  gm is the transconductance and gd is the output conductance of the MOSFET.  The values of these parameters are bias dependent and can be calculated by performing small-signal analysis at different DC operating (bias) points.

 

Small-signal equivalent circuit

Small-signal equivalent circuit

 

Input Impedance

Download the nmos_ac.ldev project file and the nmos_Zin.lsf script file in the same folder.  Run the nmos_Zin.lsf script file.  The script file will set up the dc bias to apply 5 V at the drain and sweep the gate voltage from 0 to 2 V in 11 steps.  At bias point VD = 5 V and VG = 2 V a small signal ac voltage of 0.001 V is applied at the gate.  The frequency of the small-signal voltage is swept from 1 MHz to 20 GHz.  The script will automatically run the simulation and calculate the input impedance Zin = Vg/Ig.  The figure below shows the magnitude and angle of Zin plotted by the script.  It also saves the impedance values in a .mat file.

 

Magnitude of input impedance

Magnitude of input impedance

Angle of input impedance

Angle of input impedance

 

The input impedance of the MOSFET primarily comes from the gate capacitance (Cgs and Cgd) as evident from the equivalent circuit.  This is also reflected in the input impedance plots.  The angle of Zin shows that (at low frequencies) the input impedance is purely capacitive.  The channel introduces a small resistance in series with Cgs that becomes comparable to the reactance at extremely large frequency only.

 

Output Impedance

Download the nmos_Zout.lsf script file in the same folder as the other files.  In this case, the script applies a small signal ac voltage at the drain contact for a DC bias of VD = 5 V and VG = 2 V.  Running the script will run the nmos_ac.ldev file and calculate output impedance Zout = Vd/Id.  The figure below shows the output impedance of the MOSFET as a function of frequency plotted by the script.  The script will also save the output impedance values on a .mat file.

 

Magnitude of output impedance

Magnitude of output impedance

Angle of output impedance

Angle of output impedance

 

The output impedance of the MOSFET is primarily due to the drain-source conductance (gd) as can be seen from the equivalent circuit.  This is also seen in the plots of the output impedance above.  At low frequencies the output impedance is purely resistive.  As large frequencies however the reactance from Cgd becomes smaller and the input impedance becomes capacitive.

 

Unity-Current-Gain Cutoff Frequency

The unity current gain cutoff frequency or fT is a widely accepted figure of merit in determining the bandwidth of a MOSFET.  As the name suggests, it denotes the frequency at which the current gain becomes 1.  Download the nmos_fT.lsf script file and run it.  The script will set the drain voltage to 5 V and sweep the gate voltage from 0 to 2.5 V.  At each bias point, it applies a small signal voltage at the gate and calculates the current gain Ai = Id/Ig.  Finally the script calculates the fT by identifying the frequencies where the current gain becomes unit and plots it as a function of gate bias.

 

Unity-current-gain cutoff frequency

Unity-current-gain cutoff frequency

 

Small-Signal Equivalent Circuit

By inspecting the small-signal equivalent circuit of the MOSFET, the input impedance can be defined as,

where Cgg is the sum of the gate capacitances Cgs and Cgd.  Similarly, the output impedance of the MOSFET can be defined as,

Finally, the unity-current-gain cutoff frequency of the MOSFET can be defined as,

Thus, by inspecting the values if Zin, Zout, and fT, the small-signal circuit parameters can be calculated.  Download the script file nmos_small_signal_parameters.lsf and run it.  The script file loads the data saved by the previous scripts and calculates the circuit parameters for the MOSFET.

 

Transconductance versus frequency

Transconductance versus frequency

Drain (output) conductance versus frequency

Drain (output) conductance versus frequency

Cgs versus frequency

Cgs versus frequency

Cgd versus frequency

Cgd versus frequency

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