Chapter 2 Small-Signal Amplifier

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Contents

Bipolar Transistor Amplifiers

Common-Emitter Amplifier

Common Base Amplifier

Emitter Follower

Field-Effect Transistors Amplifiers

Common-Source Amplifier

Source-Follower

Common-Gate Amplifier

Multistage Amplifiers

Dual Gate FET

Push Pull Amplifiers

Differential Amplifier

Common Mode

Analysis of Differential Amplifiers

FET Differential Amplifier

• The equivalent circuit of the BJT is shown Fig. 2-1
• r_b¡¦ is the resistance between the terminal and the actual base junction, r_p is the base-emitter junction resistance. Typically r_p >> r_b¡¦. An estimation of r_p is
• r₀ is the collector to emitter resistance typically of the order 15kƒW, r_m is the collector-base resistance of the order several MW
• The transconductance g_m r_m = b

  

• A simplified version of the small-signal model equivalent circuit is given Fig. 2-2

Common-Emitter Amplifier

• Fig. 2-3
• 
• here the coupling capacitance is treated as a short circuit.
• The output voltage is therefore



• The input impedance, not including R_s, is given be



• Since r_p depends on applied the input resistance will depend on it as well.
• The current gain is

  

Common Base Amplifier

• The Circuit diagram and its equivalent circuit model for the CB amplifier are shown in Fig. 2-4
• Since the sum of the currents leaving the emitter junction is 0, we have the following expression
• If r0 is assumed to be large compared with R_s, r_pà and R_L, the voltage gain is

  

• if r_p>> R_s(1+ƒb), the magnitude of the voltage gain will be the same as that of the common-emitter amplifier
• The input impedance of the common-base amplifier is determined using the following circuit

  

• Fig. 2-5
• The output impedance is determined using the following circuit

  

• Fig. 2-6
• The common-base amplifier has a voltage gain but its current gain is less than unity. It is used as non-inverting amplifiers where low input impedance and high output impedance is desired.
• It also has much better high-frequency response than CE amplifier and is often used in high-frequency circuits.

Emitter Follower

• The EF has a non-inverting voltage gain of less than 1
• However, it can combine with other stages, such as the CE stage, to realize a greater combined gain than CE stage alone
• Fig. 2-7 , Fig. 2-8 and Fig. 2-9
• Using the equivalent circuit the voltage gain if found to be

  

• EF configuration has the largest input impedance compared to the other configurations
• The output impedance is

  

• EF is used when low output impedance is needed. Also, although it has a voltage gain < 1, it has large current gain. It is frequently used as a power amplifier for low-impedance loads.

Field-Effect Transistors Amplifiers

• There are two types of FETs -- JFETs and MOSFETs.
• The low-frequency small signal model is as shown in Fig. 2-10
• The transconductance is defined as
• For JFETs
• where g_m0 is the transconductance when gate-to-source bias voltage is 0, I_D is the drain current and I_DSS is the drain current when the gate-to-source voltage is 0.
• For MOSFETs, g_m is
• where g_mR is the transconductance at some specified drain bias current I_DR

Common-Source Amplifier

• The common-source amplifier is similar to the common-emitter amplifier
• Fig. 2-11
• Normally R_g >> R so V_i = V_g
• The source voltage is determined from the following equations

  

• since the current leaving output node and source is zero
• The current through R_s The source voltage is



• The voltage gain is

  

• If rd >> R_s and R_L we have the following relationship

  

• For gm R_s >> 1 we have

  

Source-Follower

• The circuit diagram and its equivalent circuit model for source follower are shown in Fig. 2-12
• If R_b >> R_s, then

  

• The output impedance is

  

• which is much smaller than the other two FET amplifier configurations and is the major advantage for this configuration

Common-Gate Amplifier

• The common-gate amplifier is often used in high-frequency application and has a much larger bandwidth than the common source configuration.
• Fig. 2-13
  • 

• Thus

   

• The input impedance at the source can be found by solving for the source current

  

• and
• since

  

• The output impedance is determined as

• but I₀ is also the current passing through the source resistance so

  

• The common gate amplifier has the highest output impedance of the three FET amplifier

Multistage Amplifiers

• Multistage amplifiers are used for impedance matching or to obtain extra gain.
• Power transistors have smaller gain-bandwidth product than low-power transistors, hence the power amplification stage is often operated near unity voltage gain in order to maximize the bandwidth
• Voltage amplification is carried out in the stages preceding the power amplification stage

Dual Gate FET

• The FET cascode circuit has many high-frequency applications that two FETs are often fabricated as a single transistor with 2 gates. The source of the one transistor is continuous with the drain of the other so the device has 1 source, 1 drain and 2 gates
• The device offers low-noise and high gain in radio-frequency applications
• It is a versatile device which can be used as a mixer or automatic gain control amplifier. The equivalent circuit is as shown in Fig. 2-14
• Here gate 2 and the source are grounded
• The load resistance of the first stage is the input resistance of the second stage, and the second stage is a common-gate amplifier. Therefore
• Since

  

• where g_mR is the transconductance at some specified drain bias current IDR.
• Since both transistors have the same drain current g_m1=g_m2. Thus V_i=-V_D1 and V_gs2=-V_s2=-V_D1

  

Push Pull Amplifiers

• Transistors all exhibit a nonlinear characteristic that causes distortion of the input signal levels. Such distortion can be eliminated by push-pull amplifier
• Fig. 2-15
• The above example uses 2 center-tapped transformers. The input transformer separates the input signal into 2 signal 180^o out of phase. The output transformer is used to sum the output currents of the two transistors.
• Hence

  

• If the input signal is V_i = A cos wt
• then the output of the 2 transistors are also periodic, and they can be expressed in a Fourier series

  

• If the two transistors are identical then I₁ and I₂ are identical except I₂ lags I₁ by 180^o. Thus
• The output current is

  

• The even harmonics are eliminated from the output. This is important as FET have a square-law characteristic that generates a relatively large second harmonic.

Differential Amplifier

• The differential amplifier is an essential building block in modern IC amplifiers. The circuit is shown Fig. 2-16
• The operation of this circuit is based on the ability to fabricate matched components on the same chip. In the figure I_EE is realized using a current mirror. We assume that Q₁ and Q₂ are identical transistors and both collector resistors fabricated with equal values.
• The KVL expression for the loop containing the two emitter-base junctions is

  

• The transistors are biased in the forward-active mode, the reverse saturation current of the collector-base junction is negligible. The collector currents IC1 and IC2 are given by

  

• where we assumed that exp(V_bb/kT) >> 1

  

• where Vd is the difference between the two input voltages. KCL at the emitter node requires

  

• Similarly , The transfer characteristic for the emitter-coupled pair is shown in Fig. 2-17
• If V_d = 0 then I_C1 = I_C2
• If we incrementally increase V₁ by Dv/2and simultaneously decrease V₂ by Dv/2. The differential voltage becomes Dv. For Dv< 4kT as indicated in the transfer characteristics above the circuit behaves linearly. I_C1 increases by DI_C and I_C2 decreases by the same amount.

Common Mode

• Consider both V₁ and V₂ are increased by Dv/2. The difference voltage remains 0, and I_C1 and Ic2 remain equal. However, both I_C1 and I_C2 exhibit a small increase dI_C. Hence the current in R_E increases by 2dI_C. The voltage V_E is no longer constant but increase by an amount of 2dI_CR_B. This situation where equal signal are applied to Q₁ and Q₂ is the called the common mode.
• Usually differential amplifiers are designed such that only differential signals are amplified.

Analysis of Differential Amplifiers

• The analysis of differential amplifiers is simplified using ¡§half-circuit¡¨ concept. The equivalent circuit model for differential and common modes are shown in Fig. 2-18
• Differential mode gain
• Common mode gain is
• The Common Mode Rejection Ration (CMRR) is defined as
• From the above we obtain
• If arbitrary signals V1 and V2 are applied to the inputs then

  

FET Differential Amplifier

• A typical differential amplifier connection is shown in Fig. 2-19 and Fig. 2-20