# Department of EECS University of California, Berkeley EECS 105 Fall 2003, Lecture 16 Lecture 16: Small Signal Amplifiers Prof. Niknejad.

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Department of EECS University of California, Berkeley EECS 105 Fall 2003, Lecture 16 Lecture 16: Small Signal Amplifiers Prof. Niknejad

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Lecture Outline Review: Small Signal Analysis Two Port Circuits – Voltage Amplifiers – Current Amplifiers – Transconductance Amps – Transresistance Amps Example: MOS Amp Again!

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small Signal Analysis Step 1: Find DC operating point. Calculate (estimate) the DC voltages and currents (ignore small signals sources) Substitute the small-signal model of the MOSFET/BJT/Diode and the small-signal models of the other circuit elements. Solve for desired parameters (gain, input impedance, …)

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley A Simple Circuit: An MOS Amplifier Input signal Output signal Supply “Rail”

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Analysis Step 1. Find DC Bias – ignore small-signal source V GS,BIAS was found in Lecture 15 I GS,Q

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Modeling What are the small-signal models of the DC supplies? Shorts!

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Models of Ideal Supplies Small-signal model: short open

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Circuit for Amplifier

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Low-Frequency Voltage Gain Consider first   0 case … capacitors are open-circuits Transconductance Design Variable Design Variables

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Voltage Gain (Cont.) Substitute transconductance: Output resistance: typical value n = 0.05 V -1 Voltage gain:

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Input and Output Waveforms Output small-signal voltage amplitude: 14 x 25 mV = 350 Input small-signal voltage amplitude: 25 mV

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley What Limits the Output Amplitude? 1. v OUT (t) reaches V SUP or 0 … or 2. MOSFET leaves constant-current region and enters triode region

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Maximum Output Amplitude v out (t)= -2.18 V cos(  t)  v s (t) = 152 mV cos(  t) How accurate is the small-signal (linear) model? Significant error in neglecting third term in expansion of i D = i D (v GS )

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Generalized Amplifier Active Device

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Amplifier Terminology Sources: Signal, its source resistance, and bias voltage or current Load: Use resistor in Chap. 8, but could be a general impedance Port: A pair of terminals across which a voltage andan associated current are defined Source, Load: “one port” Amplifier: “two port”

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley One-Port Models (EECS 40) A terminal pair across which a voltage and associated current are defined Circuit Block

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Two-Port Models We assume that input port is linear and that the amplifier is unilateral: – Output depends on input but input is independent of output. Output port : depends linearly on the current and voltage at the input and output ports Unilateral assumption is good as long as “overlap” capacitance is small (MOS)

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Math 54 Perspective Can write linear system of equations for either i out or v out in terms of two of i in, v in, i out, or v out : possibilities are What is physical meaning of  1 ? of  6 ?

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley EE Perspective Four amplifier types: determined by the output signal and the input signal … both of which we select (usually obvious) – Voltage Amp (V  V) – Current Amp (I  I) – Transconductance Amp (V  I) – Transresistance Amp (I  V) We need methods to find the 6  parameters for the four models and equivalent circuits for unilateral two ports

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Two-Port Small-Signal Amplifiers Current Amplifier Voltage Amplifier

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Two-Port Small-Signal Amplifiers Transresistance Amplifier Transconductance Amplifier

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Input Resistance R in Looks like a Thevenin resistance measurement, but note that the output port has the load resistance attached

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Output Resistance R out Looks like a Thevenin resistance measurement, but note that the input port has the source resistance attached

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Finding the Voltage Gain A v Key idea: the output port is open-circuited and the source resistance is shorted

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Finding the Current Gain A i Key idea: the output port is shorted and the source resistance is removed

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Finding the Transresistance R m

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Finding the Transconductance G m

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Common-Source Amplifier (again) How to isolate DC level?

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley DC Bias Neglect all AC signals 5 V 2.5 V Choose I BIAS, W/L

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Load-Line Analysis to find Q Q

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Small-Signal Analysis

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Two-Port Parameters: Find R in, R out, G m Generic Transconductance Amp

EECS 105 Fall 2003, Lecture 16Prof. A. Niknejad Department of EECS University of California, Berkeley Two-Port CS Model Reattach source and load one-ports:

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