BJT Amplifiers (cont’d)

Common-base topology

OUTLINE

• Common-base topology– CB core– CB stage with source resistance– Impact of base resistance

• CB stage with biasing– Emitter follower (Common-collector amplifier)– Analysis of emitter follower core– Impact of source resistance– Impact of Early effect

• Emitter follower with biasing

Reading: Chapter 5.3.2, 5.3.3-5.4

Common Base (CB) Amplifier

The base terminal is biased at a fixed voltage; the input signal is applied to the emitter, and the output signal sensed at the collector.

Small-Signal Analysis of CB Core

The voltage gain of a CB stage is gmRC, which is identical to that of a CE stage in magnitude and opposite in phase.

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Tradeoff between Gain and Headroom

To ensure that the BJT operates in active mode, the voltage drop across RC cannot exceed VCC-VBE.

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Cv V

VVR

V

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Simple CB Stage Example

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VCC = 1.8VIC = 0.2mAIS = 5x10-17 A = 100

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Input Impedance of a CB Stage

The input impedance of a CB stage is much smaller than that of a CE stage.

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CB Stage with Source Resistance

With the inclusion of a source resistance, the input signal is attenuated before it reaches the emitter of the amplifier; therefore, the voltage gain is lowered. This effect is similar to CE stage emitter degeneration.

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m

Cv

Rg

RA

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Practical Example of a CB Stage

An antenna usually has low output impedance; therefore, a correspondingly low input impedance is required for the following stage.

Output Impedance: CE vs. CB Stages

The output impedances of emitter-degenerated CE and CB stages are the same. This is because the circuits for small-signal analysis are the same when the input port is grounded.

Output Impedance of a CB Stage

The output impedance of a CB stage is equal to RC in parallel with the impedance looking into the collector.

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Av of CB Stage with Base Resistance (VA = ∞)

With base resistance, the voltage gain degrades.

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Voltage Gain: CE vs. CB Stages

The magnitude of the voltage gain of a CB stage with source and base resistances is the same as that of a CE stage with base resistance and emitter degeneration.

Rin of CB Stage with Base Resistance (VA = ∞)

The input impedance of a CB stage with base resistance is equal to 1/gm plus RB divided by (+1). This is in contrast to a degenerated CE stage, in which the resistance in series with the emitter is multiplied by (+1) when seen from the base.

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Input Impedance Seen at Emitter vs. Base

Common Base Stage Common Emitter Stage

Input Impedance Example

To find RX, we have to first find Req, treat it as the base resistance of Q2 and divide it by (+1).

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Biasing of CB Stage

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RE is necessary to provide a path for the bias current IE to flow, but it lowers the input impedance.

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Reduction of Input Impedance Due to RE

The reduction of input impedance due to i1 is undesirable because it shunts part of the input current to ground instead of to Q1 (and RC).

Choose RE >> 1/gm , i.e. ICRE >> VT

Creation of Vb

A resistive voltage divider lowers the gain. To remedy this problem, a capacitor is inserted

between the base and ground to short out the resistive voltage divider at the frequency of interest.

Example of CB Stage with Bias

Design a CB stage for Av = 10 and Rin = 50.

Rin = 50≈ 1/gm if RE >> 1/gm

Choose RE = 500

Av = gmRC = 10 RC = 500 IC = gm·VT = 0.52mA VBE=VTln(IC/IS)=0.899V

Vb = IERE + VBE = 1.16V Choose R1 and R2 to provide Vb

and I1 >> IB, e.g. I1 = 52A CB is chosen so that (1/(+1))(1/CB) is small compared to 1/gm at the

frequency of interest.

VCC = 2.5VIS = 5x10-16 A= 100VA = ∞

BJT Amplifiers (cont’d)

Emitter Follower

Emitter Follower (Common Collector Amplifier)

Emitter Follower Core

When the input voltage (Vin) is increased by Vin, the collector current (and hence the emitter current) increases, so that the output voltage (Vout) is increased.

Note that Vin and Vout differ by VBE.

Unity-Gain Emitter Follower

In integrated circuits, the follower is typically realized as shown below. The voltage gain is 1 because a constant collector current

(= I1) results in a constant VBE; hence Vout = Vin .

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AV

Small-Signal Model of Emitter Follower

The voltage gain is less than 1 and positive.

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Emitter Follower as a Voltage Divider

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Emitter Follower with Source Resistance

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R

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AV

Input Impedance of Emitter Follower The input impedance of an emitter follower is the

same as that of a CE stage with emitter degeneration (whose input impedance does not depend on the resistance between the collector and VCC).

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xin Rr

i

vR )1(

AV

Effect of BJT Current Gain

There is a current gain of (+1) from base to emitter. Effectively, the load resistance seen from the base

is multiplied by (+1).

Emitter Follower as a Buffer The emitter follower is suited for use as a buffer

between a CE stage and a small load resistance, to alleviate the problem of gain degradation.

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Output Impedance of Emitter Follower

An emitter follower effectively lowers the source impedance by a factor of +1, for improved driving capability.

The follower is a good “voltage buffer” because it has high input impedance and low output impedance.

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mout R

R

gR ||

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1

Emitter Follower with Early Effect Since rO is in parallel with RE, its effect can be easily

incorporated into the equations for the voltage gain and the input and output impedances.

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Emitter Follower with Biasing

A biasing technique similar to that used for the CE stage can be used for the emitter follower.

Note that VB can be biased to be close to VCC because the collector is biased at VCC.

Supply-Independent Biasing By putting an independent current source at the

emitter, the bias point (IC, VBE) is fixed, regardless of the supply voltage value.

Summary of Amplifier Topologies The three amplifier topologies studied thus far have

different properties and are used on different occasions.

CE and CB stages have voltage gain with magnitude greater than one; the emitter follower’s voltage gain is at most one.

Amplifier Example #1 The keys to solving this problem are recognizing the

AC ground between R1 and R2, and using a Thevenin transformation of the input network.

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m

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Rg

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1

1

1

2

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CE stage Small-signal equivalent circuit

Simplified small-signal equivalent circuit

Amplifier Example #2 AC grounding/shorting and Thevenin transformation

are needed to transform this complex circuit into a simple CE stage with emitter degeneration.

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m

S

C

in

out

RRR

Rg

RRR

v

v

1

1

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1

||

Amplifier Example #3 First, identify Req, which is the impedance seen at

the emitter of Q2 in parallel with the infinite output impedance of an ideal current source.

Second, use the equations for a degenerated CE stage with RE replaced by Req.

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1 1

2

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gR

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Amplifier Example #4

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Cv

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Note that CB shorts out R2 and provides a ground for R1, at the frequency of interest.

R1 appears in parallel with RC; the circuit simplifies to a simple CB stage with source resistance.

Note that the equivalent base resistance of Q1 is the parallel connection of RE and the impedance seen at the emitter of Q2.

Amplifier Example #5

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R

ggR ||

1

1

1

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21