Biasing MOSFET Amplifier
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Biasing MOSFET Amplifier Biasing with resistors Adjust the values of resistors and MOSFET parameters to put the MOSFET in an operating Point such as: Biasing with constant current source Current source: ID2 is constant, Its value adjusted by the choice of R to the desired value: 1 π 2 πΏ 1 Q1 saturation βΉ πΌπ·1 = ππ′ ππΊπ − ππ‘ 2 ID1 is the current through R βΉ πΌπ·1 = πΌπ πΈπΉ = ππ·π· + πππ − ππΊπ π The current πΌπ πΈπΉ is the reference current 1 π 2 πΏ 2 If Q2 is in saturation βΉ πΌπ·2 = ππ′ Since Q2 has same VGS as Q1 then πΌπ·2 = πΌπ πΈπΉ π πΏ π πΏ 2 1 ππΊπ − ππ‘ 2 Small signal operation and models Simple conceptual MOSFET circuit: ο DC VGS applied on the Gate-Source for biasing ο A small signal vgs applied: the ac signal The DC Bias Point: Assume small signal vgs is zero ο vGS = VGS + vgs = VGS only DC 1 ο ππ· = πΌπ· = 2 ππ′ π πΏ ππΊπ − ππ‘ 2 only DC ο π£π· = ππ· = ππ·π· − π π· πΌπ· only DC To ensure proper amplifier operation MOSFET must be saturated: ⇒ ππ· > ππΊπ − ππ‘ ππ· has to be half way between VDD and ππΊπ − ππ‘ Signal current in the drain: ο vGS = VGS + vgs 1 ο ππ· = 2 ππ′ ππ· = π πΏ π£πΊπ − ππ‘ 2 1 ′ π π π − ππ‘ 2 π πΏ πΊπ 1 π 2 πΏ = ππ′ 2 + ππ′ ππΊπ + π£ππ − ππ‘ 2 π 1 π 2 ππΊπ − ππ‘ π£ππ + ππ′ π£ πΏ 2 πΏ ππ 1. First term is the DC component ID, 2. Second term has a linear dependence with the signal vgs 3. Third term has nonlinear dependence on vgs, this term is undesirable it represent nonlinear distortion: ο To reduce this distortion we need to keep the signal small such 1 π 2 π that ππ′ π£ππ βͺ ππ′ ππΊπ − ππ‘ π£ππ 2 Resulting in πΏ πΏ π£ππ βͺ 2 ππΊπ − ππ‘ or π£ππ βͺ 2πππ This is the small signal approximation ππ· ≅ πΌπ· + ππ Where π ππ = ππ′ ππΊπ − ππ‘ π£ππ πΏ the small signal component of the drain current; it is proportional to the small signal π£ππ Small signal parameter The parameter that relates ππ to π£ππ : is the MOSFET transconductance ππ ππ = Graphical Interpretation: ππ = πππ· ππ£ππ π£πΊπ =ππΊπ ππ π π = ππ′ ππΊπ − ππ‘ = ππ′ π π£ππ πΏ πΏ ππ iD Slope = gm iD Approximate iD Exacte id Q iD t IDQ VGSQ Vt vGS vgs t Voltage Gain π£π· π£π· π£π· π£π· = ππ·π· − π π· ππ· = ππ·π· − π π· (πΌπ· + ππ ) = (ππ·π· − π π· πΌπ· ) − π π· ππ = ππ· + π£π Where π£π = −ππ π π· = −ππ π£ππ π π· π΄π£ ≡ The voltage gain is: π£π π£ππ = −ππ π π· The minus sign indicate that π£π is 180 º out of phase with π£ππ vgs vd t Small Signal Equivalent Circuit: ππ = ππ π£ππ ππ΄ ππ = πΌπ· 1 π πΌπ· = ππ′ π − ππ‘ 2 πΏ πΊπ example G D gmvgs vgs 2 S ro Low frequency Equivalent circuit At low frequency no capacitive effect. G D gmvgs vgs At high frequency charging and discharging of the different capacitors have to be taken into consideration ro S G The figure shows the different capacitors in a MOSFET and where they originate: ο Cgs and Cgd : Oxide capacitance ο Csb and Cdb : Junction Capacitance S D Cgd Cgs n+ Csb n+ p type substrate B Cdb Complete high frequency small signal Equivalent circuit: Cgd g mbο΅bs g m ο΅ gs G ο΅ gs ro Cgs Cdb ο΅bs S D Csb B Body and Source connected and body effect neglected Cgd g m ο΅ gs G ο΅ gs D ro Cgs S Cdb Cdb can be neglected to give the simplified high frequency small signal Equivalent circuit Cgd g m ο΅ gs G ο΅ gs ro Cgs S D
