Voltage Gain without the bypass Capacitor Without C

Voltage Gain without the bypass Capacitor Without C 2, emitter is no longer at ac ground, instead RE is now seen by the signal between emitter and ground adds to internal re’. Av = RC/(re’+RE). Example : Calculate base-to-collector voltage gain of the amplifier both without and with an emitter bypass capacitor if there is no load resistor. Without C 2 gain is, Av = RC/(r’e+RE) = 1. 0 kΩ/6. 58Ω =1. 76 With C 2 gain is, Av = RC/r’e = 1. 0 kΩ/6. 58Ω = 152 The effect of RE is to decrease the ac voltage gain

Effect of a Load on the Voltage Gain When load RL is added at the output capacitor end C 3, effective resistance seen by the signal is RC in parallel with RL. Rc = RC//RL Replace RC with Rc, Av = Rc/re’ When Rc < RC, Av reduced, if RL >> RC, then Rc = RC and RL have little effect on Av.

Example : Calculate the base-to-collector voltage gain of the amplifier when load resistance of 5 kΩ in connected to output and RC is 1 k Ω. emitter is effectively bypassed and r’e = 6. 58Ω. ac collector resistance, Rc = RC||RL =RCRL/(RC+RL) = ((1. 0 kΩ)(5 kΩ))/6 kΩ = 833 Ω Therefore, Av = Rc/r’e = 833 Ω/6. 58 Ω = 127 unloaded gain was found to be 152

Stability of the Voltage Gain Stability is a measure of how well an amplifier maintains its design values over changes in temperature or for a transistor with a different β. Bypassing RE with capacitor causes the gain to be more dependent on re’ since (Av = RC/r’e) ; r’e depends on IE and on temperature; reduced stability. Without bypass capacitor, the gain is Av=RC/(re’+RE) and if RE is big enough. Av = RC/RE…. Which is less dependent on re’ or IE.

Swamping r’e to stabilize the voltage gain • Swamping is a method used to minimize the effect of r’e without reducing the voltage gain to it minimum value. • In a swamp amplifier, RE is partially bypassed so that a reasonable gain can be achieved and the effect of r’e on the gain is greaty reduced or eliminated. • The total external emitter resistance, RE is formed with two separate emitter resistors, RE 1 and RE 2 (RE 2 is bypassed and the other is not). Av= RC/(r’e + RE 1) = RC/RE 1 (if RE 1 is at least ten times larger than r’e then the effect of r’e is minimized)

Both resistors (RE 1 and RE 2) affects the dc bias while only RE 1 affects the ac voltage gain.

Examples : RE 2 bypassed by C 2. Assume r’e = 20 Ω and since RE 1 is more than 10 times r’e, the approximate voltage gain is So, Av = RC/RE 1 = 3. 3 kΩ/330Ω = 10

The Effect of Swamping on the Amplifier’s Input Resistance ac input resistance, with RE completely bypassed, is Rin = βacr’e When emitter resistance, partially bypassed, Rin = βac(re’+ RE 1) Vout at collector is 1800 out of phase with Vin at base, shown by – Av.

Current Gain Overall current gain of the common-emitter, Ai = Ic/Is Is is total signal current produced by the source, part of which is base current (Ib) and part of which (Ibias) goes through the bias circuit (R 1||R 2). Total current signal produce by source is, Is = Vs/(Rin(tot) + Rs) Power gain is, Ap = A’v. Ai, where A’v = Vc/Vs

3. 4 Common-Collector Amplifier Common-collector amplifier is usually referred to as the emitter follower because there is no phase inversion or voltage gain. The output is taken from the emitter. The common-collector amplifier’s main advantages are it’s high current gain and high input resistance.

Voltage Gain Input signal is capacitive coupled to base, output signal is capacitive coupled to emitter, and collector is at ac ground. No phase inversion and Vout approx same as Vin. Av = Vout/Vin, Xc are negligible at freq operation Re = RE ||RL Vout = Ie. Re and Vin = Ie(r’e + Re) Av = Re/(re’ +Re) if no load, Re = RE Gain is always less than 1. If Re >> r ’e than Av = 1 And since no inversion So called emitter-follower Emitter-follower model for voltage gain derivation

Input Resistance Because of the high input resistance it used as a buffer to reduce the loading effect when a circuit is driving a low impedance loads. Emitter resistor is never bypassed because Vout is taken across Re. Rin(base) = Vin/Iin = Vb/Ib = Ie(re’+Re)/Ib Since Ie = Ic = βIb Rin(base) = βIb(re’+Re)/Ib = β(re’+Re) If Re >> re’ so Rin(base) = βRe Rin(tot) = R 1 || R 2 || Rin(base)

Output resistance With the load removed, Rout looking at emitter of emitter follower: Rout = (Rs/ β) || RE (Rs - resistance of input source) Output resistance is very low and this makes it useful for driving low impedance loads. Current Gain Current gain for emitter follower , Ai = Ie/Iin where Iin = Vin/Rin(tot) Power Gain Power gain, Ap = Av. Ai Since Av = 1, so Ap = Ai

Darlington Pair Darlington pair is used to boost the input resistance to reduce loading of high output impedance circuits. Collectors are joined together and emitter of the input transistor is connected to the base of the output transistor. Ie 1 = βac 1 Ib 1 Ie 1 = Ib 2, so Ie 2 = βac 2 Ie 1 = βac 1βac 2 Ib 1 βac = βac 1βac 2 Neglecting r’e by assuming it is much smaller than RE (r’e<<RE) So Rin = βac 1βac 2 RE

Application Emitter-follower or buffer often used as interface between a circuit with high Rout and low RL. Example : common-emitter amp with RC = 1. 0 kΩ and RL = 8Ω If re’ = 5Ω, so Av = RC/re’ = 200 (with no load) With load; Rc = RC||RL = 1. 0 k Ω || 8 Ω = 7. 94Ω, Av = Rc/re’ = 7. 49/5 = 1. 59Ω (so not acceptable because Av is lost) So it can be used to interface the amplifier and speaker.

3. 5 Common-Base Amplifier Common-base amplifier has high voltage gain with a current gain no higher than 1. It has a low input resistance making it ideal for low impedance input sources. ac signal is applied to emitter and output is taken from the collector.

Base is the common terminal and is at ac ground because of C 2. Input signal is capacitive coupled to emitter and output is capacitive coupled from collector to RL. Voltage gain: Av = Vout/Vin = Vc/Ve = Ic. Rc/(Ie(r’e||RE)) = Ie. Rc/(Ie(r’e||RE)) If RE >> r’e, then Av = Rc/r’e where Rc = RC||RL No phase inversion from emitter to collector Input resistance (looking in emitter): Rin(emitter) = Vin/Iin = Ve/Ie = (Ie(r’e||RE))/Ie If RE >> r’e then Rin(emitter) = r’e Output resistance (looking in collector): Rout = r’c||RC Typical value rc >> RC, so Rout = RC Current gain, Ai = 1 Power gain, Ap = Av this is typical

3. 6 Multistage Amplifiers Two or more amplifiers can be connected to increase the gain of an ac signal. Basic objective is to increase overall voltage gain, Av. Overall gain can be calculated by simply multiplying each gain. A’v = Av 1 Av 2 Av 3 …… Voltage gain often expressed in decibels d. B, Av (d. B) = 20 log. Av So, A’v(d. B) = A’v 1(d. B) + A’v 2(d. B) + A’v 3(d. B) +…

Capacitively-Coupled Multistage Amplifier Use two stage capacitive coupled amplifier where capacitive coupling keeps dc bias voltages separate but allows the ac to pass through to the next stage because Xc = 0 at frequency operation. Av 1 have loading effect on stage 2. Rin(tot)2 presents an ac load to first stage because coupling capacitor C 3 appear short at signal freq. From collector Q 1, R 5 and R 6 appear parallel with Rin(base 2). In other word, signal at collector Q 1 see R 3, R 5, R 6 and Rin(base 2) of stage 2 all parallel to ac ground. Thus, effective ac collector resistance, Rc(Q 1) is total of all this resistor in parallel. A two-stage commonemitter amplifier

Av stage 1 decrease by loading of stage 2 because effective collector resistance of stage 1 is less than actual value of collector R 3. Remember, Av = Rc/re’. The ac collector resistance of the first stage, Rc 1 = R 3||R 5||R 6||Rinbase 2 The voltage gain of the first stage, Av 1 = Rc 1/re’ The voltage gain of the second stage, Av 2 = R 7/re’ Overall voltage gain, Av’ = Av 1 x Av 2

Dc voltages in the capacitively coupled multistage amplifiers Since Q 1 and Q 2 identical, the dc voltage is same. βdc. R 4 >> R 2 and βdc. R 8 >> R 6, so ; VB = R 2/(R 1 + R 2) x VCC VE = VB – 0. 7 IE = VE/R 4 IC = I E VC = VCC – ICR 3

Direct coupled Multistage Amplifiers For direct-coupled multi stage amplifiers, there are no coupling and no bypass capacitor in the circuit. dc collector voltage of stage 1, provide basebias voltage for stage 2. It’s has better low-frequency response than capacitive coupled type in which reactance of coupling and by-pass capacitor are increase. The increased reactance of capacitors at lower frequencies produces gain reduction in capacitively coupled amplifiers. So the amplifiers are used to amplify low frequency without gain loss because no capacitive reactance in circuit. The disadvantage is that small changes in dc bias from temperature changes or supply variations are amplifier by succeeding stage, which result in drift in dc level in circuit.