lab 7

Diff. Amp. dc Analysis ac Analysis

BJT Differential Amplifier

A differential amplifier circuit has two input terminals (v1,v2), and a differential-mode output voltage (VoD ) defined as the voltage difference between the collectors of the two transistors.

Ground-referenced outputs can also be taken between collector and drain i.e.vC 1 and vC 2

Differential amplifier behaves as either an inverting or non-inverting amplifier for differential input signals but tends to reject signals common to both inputs.

However, ideal performance is obtained from the differential amplifier only when it is perfectly symmetrical, and the best versions are built using IC technology in which the transistor characteristics can be closely matched.

Figure 1: BJT Differential Amplifier

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Diff. Amp. dc Analysis ac Analysis

dc Analysis of the Bipolar Differential Amplifier

Calculating β

β = α

1 − α (1)

α = IC

IE (2)

Transconductance

gm = IC

VT (3)

where, VT is thermal voltage (26mV)

Internal resistance

rπ = β

gm (4)

Figure 2: Circuit for dc analysis of the bipolar differential amplifier.

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Diff. Amp. dc Analysis ac Analysis

ac Analysis of the Bipolar Differential Amplifier

The ac analysis of the differential amplifier can be simplified by breaking input sources v1 and v2 into their equivalent differential-mode input (vid ) and common-mode input (vic ) signal components,defined by

vid = v1 − v2 (5)

vic = v1 + v2

2 (6)

The total input voltages can be written in terms of vic and vid as

The differential-mode input signal is the difference between inputs v1 and v2, whereas the common mode input is the signal that is common to both inputs.

Figure 3: Definition of the differential mode (vid ) and common mode (vic ) input voltages.

The differential-mode vod and common-mode output voltages voc are defined as

vod = vc1 − vc2 (7)

voc = vc1 + vc2

2 (8)

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Diff. Amp. dc Analysis ac Analysis

vod and voc are the the function of both vid and vic and can be written as[ vod voc

] =

[ Add Acd Adc Acc

] [ vid vic

] (9)

where, Add = differential-mode gain Acd = common-mode (to differential-mode) conversion gain Acc = common-mode gain Adc = differential-mode (to common-mode) conversion gain

For an ideal symmetrical amplifier with matched transistors, Acd and Adc are zero, and above equation reduces to

[ vod voc

] =

[ Add 0

0 Acc

] [ vid vic

] (10)

If either vc1 or vc2 alone is used as the output, referred to as a single-ended (or ground-referenced) output, then

Add1 = − gmRC

2 (11)

Add2 = + gmRC

2 (12)

Add = −gmRC (13)

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Diff. Amp. dc Analysis ac Analysis

Differential-Mode Input Resistance

Rid = 2rπ (14)

Common-mode gain

Acc = RC

2REE (15)

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