EKT104 ANALOG ELECTRONIC CIRCUITS [LITAR ELEKTRONIK ANALOG] BASIC BJT AMPLIFIER (PART I) DR NIK ADILAH HANIN BINTI ZAHRI adilahhanin@unimap.edu.my

Analog Signals & Linear Amplifiers Natural analog signals: physical sense (hearing, touch, vision) Electrical analog signals: e.g. output from microphone, output signal from compact disc - form of time-varying currents & voltages Magnitude: any value which vary continuously with time Analog circuits Electronic circuits which produce analog signals E.g. linear amplifier Linear amplifier Magnifies input signal & produce output signal that is larger & directly proportional to input signal DC voltage source Low signal power High signal power DC power Block diagram of a compact disc player system (a) (b) Signal source Amplifier Load

The Bipolar Linear Amplifier (a) Bipolar transistor inverter circuit; (b) inverter transfer characteristics To use circuit as an amplifier, transistor needs to be biased with DC voltage at quiescent point (Q-point)  transistor is biased in forward active operating mode Time-varying output voltage is directly proportional to & larger than time-varying input voltage  linear amplifier Fig (a) shows the circuit where the input signal vi, contains both ac and dc signal. Vcc is dc voltage to bias the transistor at particular Q point. Q point : Steady state voltage or current at a specific terminal of an active device with no input signal applied. Forward active mode : BE junction is forward bias, where positive terminal connected to P region, and BC junction is reversed bias, where positive terminal is connected to n region. If time varying input signal is superimposed on dc input voltage, the output voltage will changed. If the output voltage is directly proportional to or larger than time varying input voltage, then the circuit is linear amplifier.

The Bipolar Linear Amplifier Variable Meaning iB, vBE Total instantaneous values IB, VBE DC values ib, vbe Instantaneous ac values Ib, Vbe Phasor values Summary of notation

Graphical Analysis & AC Equivalent Circuit RB vs vO VBB VCC iC vCE vBE iB In figure d, the sinusoidal signal source, vs will produce ac base current superimposed on q point base current. Then, the base current will induced ac collector current superimposed on q point collector current. Then, the collector current will produce voltage across Rc and induces ac collector emitter voltage. The ac collector emitter output voltage will be larger than input signal. Hence, the circuit is amplifier circuit and amplification occurred. Figure (c) (c) Common-emitter circuit with time varying signal source in series with base dc source Figure (d) (d) Common-emitter transistor characteristics, dc load line, and sinusoidal variation in base current, collector current, and collector-emitter voltage

Graphical Analysis & AC Equivalent Circuit Base on Figure (c) & (d) (time-varying signals linearly related & superimposed on dc values) If signal source, vs = 0:

Graphical Analysis & AC Equivalent Circuit For B-E loop, considering time varying signals: Rearrange: Base on (5), left side of (7) is 0. So:

Graphical Analysis & AC Equivalent Circuit For C-E loop, considering time varying signals: Base on (6), left side of (11) is 0. So:

Graphical Analysis & AC Equivalent Circuit Definition of small signal Small signal : ac input signal voltages and currents which are in the order of ±10 percent of Q-point voltages and currents. e.g. If dc current is 10 mA, the ac current (peak-to-peak) < 0.1 mA.

Graphical Analysis & AC Equivalent Circuit Rules for ac analysis Replacing all capacitors by short circuits Replacing all inductors by open circuits Replacing dc voltage sources by ground connections Replacing dc current sources by open circuits

Graphical Analysis & AC Equivalent Circuit Equations Base-emitter loop (Input loop) Collector emitter loop (Output loop) RC RB vs vO vce vbe ic ib + - Thermal voltage, 0.026 AC equivalent circuit of C-E with npn transistor (ac equivalent circuit of Figure (c))

Small-signal Hybrid- Equivalent Circuit vbe = ibrπ rπ = diffusion resistance / base-emitter input resistance 1/rπ = slope of iB – VBE curve gm=ICQ/VT r=VT/ICQ To do analysis against small signal, small signal equivalent circuit must be developed for the transistor. One way is to use hybrid-pi model which is similar to the physics of the transistor. The sinusoidal signal is small and the slope at Q-point can be treated as constant which has unit of conductance. The inverse of this conductance is the small signal resistance defined as r-pi. Therefore, the small signal input voltage is the product of small signal current and the small signal resistance. Transconductance is the ratio of the current variation at the output to the voltage variation at the input. Small signal hybrid-π equivalent circuit for npn transistor using transconductance (gm) parameter

Alternative Form of Small-signal Hybrid- Equivalent Circuit Small signal collector current can be related with small-signal base current and is called as ac common emitter current gain, beta. The figure shows the same circuit with the previous circuit. The difference is , instead of using transconductance parameter, this circuit use common emitter current gain parameter. Where beta= ic/ib Using common-emitter current gain (β) parameter

Constructing Small-signal hybrid- RC RB vs vO VBB VCC We know that i across B  ib i across C βib i across E  (β+1)ib rπ between B -E Place a terminal for the transistor Common Terminal as ground B E C βib When incorporating small signal hybrid-pi model of transistor into ac equivalent circuit, it is easier to start with 3 terminals of the transistor. Then sketch the hybrid-pi equivalent circuit to this terminals. Connect the remaining circuit elements such as Rb & Rc. This technique will minimize errors in developing the small signal equivalent circuit. B E C rπ

Small-signal Voltage Gain r Vs RB RC Vo Ic Ib gmVbe Vbe Vce + - Output signal voltage Input signal voltage

Voltage Gain Measurement RC RB vs vO VBB VCC Example Given :  = 100, VCC = 12V VBE = 0.7V, RC = 6k, RB = 50k, and VBB = 1.2V Calculate the collector-emitter voltage at q-point and small-signal voltage gain.

SOLUTIONS 1. 2. 3. 4. 5. 6.

Hybrid- Model and Early Effect Collector voltage has some effect on collector current Collector current increases slightly with increases in voltage  Early Effect Modeled as a linear increase in total current with increases in VCE The Early effect is the variation in the width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage. In small signal equivalent circuit, collector current is vary with the collector emitter voltage. The figure shows the small signal model of BJT, which include output resistance due to early effect for the case of tranconductance in upper figure. And current gain parameter in lower figure.

Hybrid- Model and Early Effect Early Voltage (pg 296) Early Voltage (VA)

Hybrid- Model and Early Effect transconductance parameter ro=VA/ICQ The Early effect is the variation in the width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage. In small signal equivalent circuit, collector current is vary with the collector emitter voltage. The figure shows the small signal model of BJT, which include output resistance due to early effect for the case of transconductance in upper figure. And current gain parameter in lower figure. current gain parameter ro = small-signal transistor output resistance VA = early voltage

Basic Common-Emitter Amplifier Circuit vs RS R1 R2 RC CC vO VCC Example Given :  = 100, VCC = 12V VBE(on) = 0.7V, RS = 0.5k, RC = 6k, R1 = 93.7k, R2 = 6.3k and VA = 100V. Calculate the small-signal voltage gain.

SOLUTION Small-signal equivalent circuit R1 \\ R2 Vs RS RC rO r gmV Vo Ri Ro Ans: ICQ = 0.95mA, VCEQ =6.3V, Av =-163)

Exercise The circuit parameters in Figure are changed to VCC = 5V, R1=35.2kΩ, R2=5.83kΩ, RC=10kΩ and RS =0, β =100, VBE(on) =0.7V and VA =100V. Determine the quiescent collector current and collector-emitter voltage and find the small-signal voltage gain. Ans: ICQ = 0.21mA, VCEQ =2.9V, Av =-79.1)

Self-Reading Textbook: Donald A. Neamen, ‘MICROELECTRONICS Circuit Analysis & Design’,3rd Edition’, McGraw Hill International Edition, 2007 Chapter 5:The Bipolar Junction Transistor Page: 334-339 Chapter 6: Basic BJT Amplifiers Page: 370-388.