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**SMALL SIGNAL BJT AMPLIFIER**

SMALL SIGNAL OPERATION

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INTRODUCTION One of the primary uses of a transistor is to amplify ac signals. This could be an audio signal or perhaps some high frequency radio signal. It has to be able to do this without distorting the original input. Most transistors amplifiers are designed to operate in the linear region The common-emitter amplifier has high voltage and current gain

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**Definition of Small Signal**

ac input signal voltages and currents are in the order ±10% of Q-point voltages and currents. eg If dc current is 10mA, the ac current (peak to peak) is less than 0.1 mA.

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HOW BJT AMPLIFIES? When a weak ac signal is given to the base, a small ac base current start flowing. Due to BJT, a much larger ac current flow through RC Therefore a large voltage appear across the collector circuit.

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**R1, R2, RE – form the biasing circuit & stabilization.**

C1(Coupling capacitor) – couple the signal to the base. C2(Bypass capacitor) - use in parallel with RE to provide low reactance path to amplified ac signal C3(Coupling capacitor)- couple the signal to the next stage

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**Circuit Diagram IC VCE IB VCC Common-Emitter Biasing(CE)**

input = VBE & IB output = VCE & IC + _ IC VCE IB VCC = Common-emitter current gain = = Common-base current gain = The relationships between the two parameters are:

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Example Given the common-emitter circuit below with IB = 25A, VCC = 15V and = 100. Find the ideal collector current. = 100 = IC/IB IC = 100 * IB = 100 * (25x10-6A) = 2.5 mA

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**Collector-Current Curves**

Common-Emitter Collector-Current Curves IC Active Region IB Saturation Region Cutoff Region IB = 0 Region of Operation Description Active Small base current controls a large collector current Saturation VCE(sat) ~ 0.2V, VCE increases with IC Cutoff Achieved by reducing IB to 0, Ideally, IC will also equal 0. VCE

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**DC Analysis of Transistor Circuits Common-Emitter Circuit**

Common-emitter circuit with an npn transistor Assume B-E junction: forward biased V drop is the cut-in / turn-on V [VBE (on)] IC represented as a dependent I source (function of IB) Neglect reverse-biased junction leakage current & Early effect

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**dc equivalent circuit, with piecewise linear parameters**

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**Base-emitter Junction Characteristics And The Input Load Line**

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**Common- Emitter Transistor Characteristics And The Collector-emitter Load Line**

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**Common-emitter circuit Load Line**

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**Kirchoff’s voltage law equation (around B-E loop):**

Both load line & quiescent IB change as either or both VBB & RB change Kirchoff’s voltage law equation (around C-E loop): IC & VCE relationship represents DC load line

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Amplifier Operation The boundary between cutoff and saturation is called the linear region. A transistor which operates in the linear region is called a linear amplifier. Only the ac component reaches the load because of the capacitive coupling and that the output is 180º out of input phase. Fig 6-2 amplifier circuit

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Example Assume Q-point value of iB=10A, ac signal peak value is 5A and β=100. So at any instant, iC =100iB iB iC=100iB VCE=VCC-iCRC Output voltage 15A 1.5mA 4 V Positive peak value 10A 1.0mA 6 V Signal current zero 5A 0.5mA 8 V Negative peak value

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**dc equivalent circuit of transistor amplifier**

Only dc condition are to be considered No signal is applied (All ac source reduce to zero) dc cannot flow through a capacitor (open circuit) To calculate the dc currents & voltages

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**DC Equivalent for the BJT Amplifier**

DC Equivalent Circuit All capacitors in the original amplifier circuit are replaced by open circuits, disconnecting vI, RI, and R3 from the circuit and leaving RE intact. The the transistor Q will be replaced by its DC model.

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**ac equivalent circuit of transistor amplifier**

Only ac condition are to be considered dc voltage not important, considered zero or ground. (VCC=0) the capacitors used to couple or bypass the ac signal. (short circuit)

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**AC Equivalent for the BJT Amplifier**

The coupling and bypass capacitors are replaced by short circuits. The DC voltage supplies are replaced with short circuits, which in this case connect to ground.

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(continued) By combining parallel resistors into equivalent RB and R, the equivalent AC circuit above is constructed. Here, the transistor will be replaced by its equivalent small-signal AC model (to be developed).

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**Graphical Analysis & AC Equivalent Circuit**

Equations Input loop Output loop RC RB vs vO vce vbe ic ib + - 0.026 V AC equivalent circuit of C-E with npn transistor

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**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 Using transconductance (gm) parameter

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**Small-signal hybrid- equivalent circuit**

Using common-emitter current gain (β) parameter

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**Small-signal equivalent circuit**

Small-signal hybrid- equivalent circuit Small-signal equivalent circuit r Vs RB RC Vo Ic Ib gmVbe Vbe Vce + - Output signal voltage Input signal voltage

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**Example Given : = 100, VCC = 12V VBE = 0.7V, RC = 6k,**

RB = 50k, and VBB = 1.2V Calculate the small-signal voltage gain. RC RB vs vO VBB VCC

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Solutions 1. 2. 3. 4. 5. 6.

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**Hybrid- Model and Early Effect**

transconductance parameter ro=VA/ICQ current gain parameter ro = small-signal transistor output resistance VA = early voltage

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**Hybrid- Model and Early Effect**

Early Voltage (pg 109) Early Voltage (VA)

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**Example vs 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. vs RS R1 R2 RC CC vO VCC

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Solution R1 \\ R2 Vs RS RC rO r gmV Vo Ri Ro

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**Exercises Neamen book: Ch. 4 Question 4.1 (pg. 177)**

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Dr. Nasim Zafar Electronics 1 - EEE 231 Fall Semester – 2012 COMSATS Institute of Information Technology Virtual campus Islamabad.

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