# Small Signal Analysis of MOS Transistor

The operation point of the transistor is called biasing. Biasing is done before performing the small-signal analysis. To bias, the transistor, positive gate voltage is applied to the transistor. In this given circuit, V_{S} is the small signal where the amplitude is low like 1mV. This circuit also shows a DC source. It has both AC and DC going into the gate of the transistor. There is load (RL) in the circuit connected to voltage V_{DD}.

The operating point for the transistor is chosen using the shown graph. V_{GS} is set for the transistor and changing the transistor size (W/L), we are getting the current I_{DS}.

As read before from the Early Voltage section in the MOS transistor for long length channel, the curve slope is almost constant in the saturation region. When L is high, λ is very low, sometimes considered 0 in the saturation region equation.

There are three curves in this graph representing V_{GS1}, V_{GS2,} and V_{GS3}. Using these, we can get the drain-source voltage, V_{DS}. Taking the reference of V_{GS2} in this case, the current is I_{D2} which is the DC point of our current as marked on the graph. Therefore, V_{DS} can be calculated as V_{DS} = V_{DD}-RL.I_{D}. Using this equation, the VDS is calculated and is the bias point. As we read before that, in saturation region V_{DS}>V_{GS} – V_{TH}, therefore V_{GS} should be more than V_{TH} (V_{GS}>V_{TH}) for the transistor to turn on and work in the saturation region. Now we got the DC values.

This figure shows the AC simulation. The transistor receives both AC & DC; shown in the circuit diagram, there is a DC source to provide the gate voltage. The DC voltage is V_{GS2}. After reaching the Q point, the AC is applied. AC can be a cosine wave with low amplitude; for example, it is 1mV (should be more than the threshold voltage V_{TH}). Hence, VG in total can be calculated as V_{G}=V_{GS2}+V_{S} = 1V+1m cos(*w*t).

The signal provided to the gate and other parts of the transistor is alternating. The graph represents the fluctuations. The alternating current limits are shown in the axis for V_{GS2}, the maximum value for this example can be 1V+1mV, and the minimum can be 1V-1mV. There is a small fluctuation in the drain current (I_{DS}) which is a small signal. It fluctuates between I_{D1} & I_{D3}; similarly, V_{DS} is fluctuating between V_{DS1} and V_{DS3}.

To represent other values like current, the DC value is I_{D2,} and for voltage, it is V_{DS2}, the amplitude for describing the current wave is I_{D3}-I_{D2,} and for V_{DS2,} the amplitude 0f the wave will be V_{DS3}-V_{DS2}.

__Defining the gm parameter__

One of the important parameter for the transistor is gm, and it is equal to the fluctuation of current (I_{DS}) to fluctuation of gate-source voltage (V_{GS}).

In the graph, the bias point V_{GS2} is plotted, for which the current bias is I_{D2}. Now we know that V_{GS} is a small signal and is changing. As shown in the graph, the fluctuation for I_{D2} has minimum values (I_{DS1} & V_{DS1}) and maximum values (I_{DS3} & V_{DS3}). The slope gm calculated for this portion will be equal to:

To summarise, in small-signal analysis, AC and DC voltage can be applied together to the gate of the transistor, and we can get the small signal for the varying current and varying drain voltage.