## XOR Gate Using Pass Transistor AC and DC Analysis

The XOR gate is a digital logic gate that outputs a logic 1 if and only if its two inputs are different. It is a fundamental building block of many digital circuits and is used in a wide variety of applications. In this article, we will analyze the XOR gate using pass transistors. We will first discuss the basic operation of the XOR gate and then we will analyze its AC and DC characteristics. ### Basic Operation of the XOR Gate The XOR gate can be implemented using two MOSFETs, as shown in the figure below.The inputs to the XOR gate are labeled A and B, and the output is labeled Y. When A and B are both 0, both MOSFETs are turned off and the output Y is 0. When A is 0 and B is 1, the upper MOSFET is turned on and the lower MOSFET is turned off, and the output Y is 1. When A is 1 and B is 0, the upper MOSFET is turned off and the lower MOSFET is turned on, and the output Y is 1. When A and B are both 1, both MOSFETs are turned on and the output Y is 0. ### AC Analysis of the XOR Gate The AC analysis of the XOR gate can be performed by using the small-signal equivalent circuit shown in the figure below.

In this circuit, the MOSFETs are represented by their small-signal equivalent circuits, and the capacitors C1 and C2 represent the parasitic capacitances of the MOSFETs. The AC input signals are labeled vA and vB, and the AC output signal is labeled vY. The AC transfer function of the XOR gate can be found by taking the ratio of the output voltage vY to the input voltage vA. ``` vY/vA = -gDS(1 + sC1C2) ``` where gDS is the transconductance of the MOSFETs and s is the complex frequency. The AC gain of the XOR gate is the magnitude of the AC transfer function. ``` |vY/vA| = gDS√(1 + s2C1C2) ``` The AC phase shift of the XOR gate is the phase of the AC transfer function. ``` φ = -tan-1(sC1C2) ``` The AC bandwidth of the XOR gate is the frequency at which the AC gain drops to 0.707 of its maximum value. ``` fBW = 1/(2πC1C2) ``` ### DC Analysis of the XOR Gate The DC analysis of the XOR gate can be performed by setting the AC input signals to zero. In this case, the output voltage vY is equal to the voltage drop across the lower MOSFET. ``` vY = VDD - RDS(on)I ``` where VDD is the supply voltage, RDS(on) is the on-resistance of the lower MOSFET, and I is the current flowing through the lower MOSFET. The DC output voltage of the XOR gate is either VDD or 0V, depending on the values of the inputs A and B. ## Conclusion The XOR gate is a versatile digital logic gate that can be used in a wide variety of applications. Its basic operation can be understood by considering the DC and AC characteristics of the circuit.

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