EE05 Fall 205 Microelectronic Devices and Circuits Prof. Ming C. Wu wu@eecs.berkeley.edu 5 Sutardja Dai Hall (SDH) 2- Amplifier Gain Voltage Gain: Current Gain: Power Gain: Note: A v v O v I A i i O i I load power A p input power v i O O v I i I A p A v A i Note: A v and A i can be positive, negative, or even complex numbers. Nagative gain means the output is 80 out of phase with input. However, power gain should always be a positive number. Gain is usually expressed in Decibel (db): A v (db) 0log A v 2 20log A v A i (db) 0log A i 2 20log A i A p (db) 0log A p 2-2
Amplifier Power Supply and Dissipation Circuit needs dc power supplies (e.g., battery) to function. Typical power supplies are designated V CC (more positive voltage supply) and -V EE (more negative supply). Total dc power dissipation of the amplifier P dc V CC I CC +V EE I EE Power balance equation P dc + P I P L + P dissipated P I : power drawn from signal source P L : power delivered to the load (useful power) P dissipated : power dissipated in the amplifier circuit (not counting load) Amplifier power efficiency η P L P dc Power efficiency is important for "power amplifiers" such as output amplifiers for speakers or wireless transmitters. 2-3 Amplifier Saturation Amplifier transfer characteristics is linear only over a limited range of input and output voltages Beyond linear range, the output voltage (or current) waveforms saturates, resulting in distortions Lose fidelity in stereo Cause interference in wireless system 2-4 2
Symbol Convention i C (t) I C + i c (t) i C (t) : total instantaneous current I C : dc current i c (t) : small signal current Usually i c (t) I c sinωt Please note case of the symbol: lowercase-uppercase: total current lowercase-lowercase: small signal ac component uppercase-uppercase: dc component uppercase-lowercase: amplitude of ac component Similarly for voltage expressions. These expressions are widely adopted, though occasionally you will find different convention. You should check carefully whenever you read a new book or paper. 2-5 Circuit Model of Voltage Amplifiers (Two-Port Model) v i v s + R v o A v0 v L R i A v0 v i s + R o + + R o Overall voltage gain: A v v o v s A v0 + + R o A v0 : open-circuit voltage gain (or voltage gain of "unloaded" amplifier) : input resistance of the amplifier R o : output resistance of the amplifier : source resistance : load resistance 2-6 3
Cascaded Amplifier For most practical applications, multiple stages of amplifiers are cascaded to provide suffiicent gain provide adequate input and output resistances For example, in a voltage amplifier the input stage is designed to have high input impedance the output stage is designed to have low output impedance middle stage(s) provide the necessary gain 2-7 Amplifier Types Depending on the nature of the source signals and output loads, different types of amplifiers are needed Voltage amplifier Current amplifier Transconductance amp Converts voltage to current Transimpedance amp Converts current to voltage The 4 models here are interchangeable, though one is usually more convenient than others for analysis 2-8 4
Amplifier Frequency Response When a sinusoidal signal is applied to a linear circuit, the output is sinusoidal with the same frequency as the input but different amplitude and phase Transfer function: Amplitude response: Phase response: T(ω) V o(ω) (ω) T(ω) V o T(ω) φ 2-9 Frequency Response Log-log plot of the transfer function versus angular frequency, ω Vertical axis: 20 log T(ω) Horizontal axis: 0 log ω This is called Bode Plot Bandwidth Band of frequencies over which the gain response falls by 3dB 2-0 5
Frequency Response of Low-Pass Filters jωc T(ω) R + + jωrc + jω /ω 0 jωc ω 0 RC T(ω) + ( ω /ω 0 ) 2 ( ) T(ω) tan ω /ω 0 ω 3dB ω 0 [rad/sec] f 3dB ω 0 2π [Hz] 2- Frequency Response of High-Pass Filters R T(ω) R + + jωc ω 0 RC T(ω) + ( ω 0 /ω) 2 T(ω) tan ω 0 /ω ω 3dB ω 0 ( ) [rad/sec] jωrc jω 0 /ω f 3dB ω 0 2π [Hz] 2-2 6
Example: Amplifier Frequency Response Z i V s + Z i Z i R / ( jωc ) i i +/ ( jωc i ) + jω V s + + jω R + + i + jωr T(ω) V o V o V s V s R µ L R o + + i + jωr K + j ω /ω 0 ω 0 R C ( ) K µ R o + + i 2-3 Typical Frequency Responses Capacitively Coupled Amplifier Direct-Coupled Amplifier Bandpass Amplifier Low frequency roll-off due to coupling capacitor High frequency cut-off due to intrinsic capacitors of the transistors 2-4 7