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Week 6 – Chapter 3 FET Small-Signal Analysis Mohd Shawal Jadin FKEE UMP © 2009 FET Small-Signal Model Transconductance The relationship of VGS (input) to ID (output) is called transconductance. The transconductance is denoted gm. Transfer Curve gm ID VGS Graphical Determination of gm Mathematical Definition of gm ID gm ΔVGS Using differential calculus I D K (VGS VTR )2 gm 2K(VGS VTR ) FET Impedance Input Impedance Zi: • Very large to assume input terminal approximate an open circuit Output Impedance Zo: yos: admittance equivalent circuit parameter listed on FET specification sheets. rd VDS ID VGS constant Zi Ω Zo rd 1 yos FET Specification FET AC Equivalent Circuit JFET Fixed-Bias Configuration The input is on the gate and the output is on the drain. JFET Fixed-Bias Configuration Once again: same step as BJT to redraw the network to AC equivalent circuit. Capacitor – short circuit DC batteries VGG and VDD are set to zero volts by a short-circuit equivalent AC Equivalent Circuit AC Equivalent Circuit Impedances Input Impedance: Zi RG Output Impedance: Zo RD || rd Zo RD rd 10RD Voltage Gain Vo Av gm(r d ||RD) Vi Vo Av gmRD Vi rd 10R D Phase Relationship A CS amplifier configuration has a 180-degree phase shift between input and output. Example Fixed-bias configuration has an operating point defined by VGSQ = -2V and IDQ = 5.625 mA, with IDSS = 10mA and VP = -8V. The value of yos is provided as 40 µS. Determine: a) gm b) Zi c) Zo d) AV e) AV ignoring the effects of rd Solution JFET CS Self-Bias Configuration This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain. AC Equivalent Circuit Impedances Input Impedance: Output Impedance: Zi RG Zo rd || RD Zo RD rd 10RD Voltage Gain Av gm(rd || RD) Av gmRD rd 10RD Phase Relationship A CS amplifier configuration has a 180-degree phase shift between input and output. JFET CS Self-Bias Configuration – Unbypassed Rs If Cs is removed, it affects the gain of the circuit. AC Equivalent Circuit Impedances Input Impedance: Output Impedance: Impedances Voltage Gain Voltage Gain Example Solution Solution JFET CS Voltage-Divider Configuration This is a CS amplifier configuration therefore the input is on the gate and the output is on the drain. AC Equivalent Circuit Impedances Input Impedance: Zi R1 || R2 Output Impedance: Zo rd || RD Zo RD rd 10RD Voltage Gain Av gm(rd || RD) Av gmRD rd 10RD JFET Source Follower (Common-Drain) Configuration In a CD amplifier configuration the input is on the gate, but the output is from the source. AC Equivalent Circuit Impedances Input Impedance: Zi RG Output Impedance: 1 Zo rd || RS || gm Zo RS || 1 gm rd 10RS Voltage Gain Vo gm(rd || RS) Av Vi 1 gm(rd || RS) Vo gmRS Av Vi 1 gmRS rd 10RS Phase Relationship A CD amplifier configuration has no phase shift between input and output. JFET Common-Gate Configuration The input is on source and the output is on the drain. AC Equivalent Circuit Impedances Applying Kirchhoff’s voltage law around the output perimeter and Kirchhoff’s current law at node a :: Impedances Input Impedance: rd RD Zi RS || 1 gmrd Zi RS || ( 1 ) gm rd 10RD Output Impedance: Zo RD || rd Zo RD rd 10RD Voltage Gain Applying Kirchhoff’s current law at node b :: RD g mRD Vo rd Av Vi RD 1 rd Av gmRD rd 10RD Phase Relationship A CG amplifier configuration has no phase shift between input and output. Depletion-Type MOSFETs 1. D-MOSFETs have similar AC equivalent models. 2. The only difference is that VSGQ can be positive for nchannel devices and negative for p-channel devices. 3. This means that gm can be greater than gm0. D-MOSFET AC Equivalent Model • Find – – – – Example VGSQ and IDQ Determine gm and compare to gm0 rd Find Zi, Zo, Av Enhancement-Type MOSFETs There are two types of E-MOSFETs: nMOS or n-channel MOSFETs pMOS or p-channel MOSFETs E-MOSFET AC Equivalent Model Forward transfer admittance gm and rd can be found in the specification sheet for the FET. E-MOSFET CS Drain-Feedback Configuration AC Equivalent Circuit Impedances Input Impedance: Zi RF 1 gmRD RF rd || RD Zi 1 gm(rd || RD) Output Impedance: Zo RF || rd || RD RF rd || RD, rd 10RD Zo RD RF rd || RD, rd 10RD The calculation From Kirchoff's Current Law at point D, Vo Ii gmVGS VGS Vin rd RD and Ii Vi Vo RF We ' ll find that, Ii Vi rd R D I i gmVi RF rearranging , Vi 1 gmrd R D I i RF rd R D so, Zi RF 1 gmRD RF rd || RD, rd 10RD Zo RF||rd||RD Zo RD RF rd||RD, rd 10RD F romKirchoff's CurrentLaw at point D, Vo Ii gmVGS VGS Vin rd RD and Ii Vi Vo RF We' ll find that, Vi Vo gmVGS Vo RF rd RD rearranging , 1 1 1 Vo V g m i rd RD RF RF so , 1 1 R gm R gm Vo F F AV gm rd RD R Vi 1 F 1 1 rd RD R F rd RD R F gmRD RF rd||RD, rd 10RD The AC analysis of E-MOSFET The relationship between output currentand controlling voltage is as below; ID k VGS VGS Th 2 We know that gm is definedby the slope of drain characteristics, gm ID VGS The derivationof above equation will determine gm at the operatingpoint; gm ID d 2 k VGS VGS Th VGS dVGS 2k VGSQ VGS Th Remember that, the biasing arrangement are limited for E-MOSFET Voltage Gain Av gm(RF || rd || RD) Av gmRD RF rd || RD, rd 10RD Phase Relationship This is a CS amplifier configuration therefore it has 180-degree phase shift between input and output. Do it •Determine input and output and also AV impedance for k=0.3X10-3 +VDD (+16V) 2.2kΩ Vo 10MΩ VGS(Th)=3V rd=100kΩ Vi Zi E-MOSFET CS Voltage-Divider Configuration AC Equivalent Circuit Impedances Input Impedance: Output Impedance: Zi R1 || R2 Zo rd || RD Zo RD rd 10RD Voltage Gain Av gm(rd || RD) Av gmRD rd 10RD Phase Relationship This is a CS amplifier configuration therefore it has 180-degree phase shift between input and output. Solution E-MOSFET CS Voltage-Divider Configuration AC Equivalent Circuit Impedances Input Impedance: 9.52] Output Impedance: 9.53] Zi R1 || R2 [Formula Zo rd || RD Zo RD rd 10RD [Formula Voltage Gain Av gm(rd || RD) Av gmRD rd 10RD [Formula 9.55] [Formula 9.56] Summary Table Summary Table Try yourself •Design a self-bias network that have gain of 10. The device should be biased at VGSQ=1/3VP +VDD (+20V) RD Vo IDSS =12mA VP=-3V rd=40kΩ Vi 10MΩ Rs Solution