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Small - Signal Model Parameters

Date：2025-06-20 Categories：Product knowledge Hits：231 From：Guangdong Youfeng Microelectronics Co., Ltd

3.1 BJT Small - Signal Model

Small-Signal Transistors The hybrid -πmodel is a commonly used small - signal model for BJTs. Key parameters in this model include:

Transconductance (gm): Defined as the change in collector current (ΔIC) divided by the change in base - emitter voltage (ΔVBE) in the small - signal regime,gm=ΔVBEΔIC. It represents the transistor's ability to convert a small change in input voltage into a changein output current. For a BJT in the activeregion,gm=VTIC, whereVTis the thermal voltage (VT≈26 mVat room temperature).nput Resistance (rπ): This is the resistance seen at the base - emitterterminals of the BJT in the small - signal model. It is related to the current gainβand the transconductancegmbyrπ=gmβ

.Output Resistance (ro): Represents the resistance seen at the collector - emitter terminals. It is due to the Early effect, which causes the effective base - width to change with the collector - base voltage. A higherrovalue means that the collector current is less affected by changes in the collector - emitter voltage.

3.2 FET Small - Signal Model

For FETs, the small - signal model also has important parameters: Small-Signal Transistors

Transconductance (gm): For a MOSFET,gmis defined as the change in drain current (ΔID) divided by the change in gate - source voltage (ΔVGS) in the small - signal regime. In the saturation region,

gm=2KnIDSS(VGS−VthVGS−Vth), whereKnis the transconductance parameter,IDSSis the drain - source saturation current, andVth

is the threshold voltage. Small-Signal Transistors

Output Resistance (ro): Similar to the BJT, the output resistance of a FET represents the resistance seen at the drain - source terminals. It accounts for the channel - length modulation effect, which causes the drain current to change slightly with the drain - source voltage even in the saturation region. Small-Signal Transistors

4. Small - Signal Analysis Methods

4.1 DC Analysis

Before performing small - signal analysis, it is necessary to conduct a DC analysis to determine the DC operating point (quiescent point) of the transistor. For a BJT amplifier circuit, this involves solving the circuit equations to find the values ofIB,IC, andVCE For a FET - based circuit, we need to find the DC values ofVGS,ID, andVDS. The DC operating point determines the region in which the transistor operates and affects the small - signal parameters. Small-Signal Transistors

4.2 AC Analysis

Once the DC operating point is established, we can replace the transistor with its small - signal model and analyze the circuit using AC circuit analysis techniques. This includes methods such as nodal analysis, mesh analysis, and the use of voltage and current divider rules. For example, in a common - emitter BJT amplifier, we can use nodal analysis at the input and output nodes to find the voltage gain (Av), input impedance (Zin), and output impedance (Zout).The voltage gain of a common - emitter amplifier can be calculated asAv=−gmrL, whererLis the load resistance seen at the collector. The input impedanceZin=rπ, and the output impedanceZout=ro. For a common - source FET amplifier, the voltage gainAv=−gmrL, the input impedance is very high (ideally infinite for a MOSFET), and the output impedance isro Small-Signal Transistors

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