MOSFET Large and Small signal Model

Introduction of Field Effect Transistors Distinction between a BJT and FET Junction Field Effect Transistor (JFET) N Channel JFET Summary of JFET Operation Mutual or Transfer Characteristic of n-channel JFET Amplification Factor 𝝁 Definition of Parameters p-Channel JFET

Introduction of Metal Oxide Semiconductor Field Effect Transistor - Mosfet Terminals in MOSFET Physical structure of MOSFET MOSFET Working Operation Summary of Operation MOSFET - N Type MOSFET Operation How does Drain current flow MOSFET operation More about Threshold Voltage Current vs Voltage Characteristics - Derivation Non Ideal Current -Voltage Effects or Second Order Effects Short Channel Effects MOSFET Device Capacitances MOSFET Large and Small signal Model pMOSFET Small SIgnal Model To use MOSFET device as a Capacitor nMOSFET as Capacitor- Working

Single Stage Amplifiers Common Source CS Stage with Diode-Connected Load Circuit to measure the Equivalent Resistance Common Drain Stage or Source Follower Common Gate Amplifier Large Signal Behavior Calculation of Input Resistance of a Common Gate Stage

Inverter with Enhancement n- Type MOS as Load Inverter with Linear Enhancement Type Load

MOSFET Large and Small signal Model

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MOSFET Large Signal Model

The discussions so far on the Drain current (quadratic characteristics) and the capacitance model in the previous section constitute the Large Signal Model. The model is used to analyze the circuits where the signal is high and thus disturbs the bias points. The model also discusses the non linear effects also.

MOSFET Small Signal Model

The change in Gate - Source Voltage VGS results in change in Drain current IDS by gmVGS.
This is modeled as a Voltage Dependent current source connected between the Source and Drain terminals
The Gate current is too small to be considered

This is an ideal MOSFET small signal model and is shown in Figure 21.

Figure 21: MOSFET Small Signal Model

Let us recollect that because of channel length modulation, the drain current also varies with the Drain Source Voltage. This can be modeled here as a voltage dependent current source.

This is shown in figure 22 below:

Figure 22: Small Signal Model showing the effect of channel length modulation - dependent current source

As the current is linearly dependent on the voltage, this can be represented by a linear resistor r0 connected between the Drain and Source.

The value of this resistor is given by:

$r_0=\frac{\partial V_{DS}}{\partial I_D}$

Using the equations developed earlier, we can rewrite the above equation as:

$r_0=\frac1{{}^{\partial ID}/\partial V_{GS}}=\frac1{{\displaystyle\frac12}\mu_nc_{OX}{\displaystyle\frac WL}\left(V_{GS}-V_{TH}\right)^2.\lambda}$

The small signal model showing the channel length modulation r₀ effect is shown in Figure 23 below.

Figure 23: MOSFET Small Signal Model showing the Channel Length Modulation effect r₀ effect

Now let us consider the effect of the body on the MOSFET functioning. It has been observed that when all other terminal voltages are held constant and the body or bulk voltage is varied, then the drain current is found to be a function of the body voltage.

In other words under such circumstances it can be assumed that the Body can be considered as a second Gate.

This effect can be modeled by a current source which is connected between Drain and Source. The dependency term used is gmb and the dependency is gmbVbs.

The term gmb is given by the equation:

$g_{mb}=\frac{\partial I_D}{\partial V_{BS}}=\mu_nC_{OX}\frac WL\left(V_{GS}-V_{TH}\right)\left(-\frac{\partial V_{TH}}{\partial V_{BS}}\right)$