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# Differential amplifier

The function of a differential amplifier is to amplify the difference between two signals.

Differential amplifier

The function of a differential amplifier is to amplify the difference between two signals. The need for differential amplifier arises in many physical measurements where response from DC to many MHz of frequency is required. This forms the basic input stage of an integrated amplifier.

The basic differential amplifier has the following important properties of

·           Excellent stability

·           High versatility and

·           High immunity to interference signals

The differential amplifier as a building block of the op-amp has the advantages of

·           Lower cost

·           Easier fabrication as IC component and

·           closely matched components. The above figure shows the basic block diagram of a differential amplifier, with two input terminals and one output terminal. The output signal of the differential amplifier is proportional to the difference between the two input signals.

V0 = Adm ( V1 – V2 )

If  V1 = V2, then the output voltage is zero. A non-zero output voltage V0 is obtained when  V1 and V2 are not equal. The difference mode input voltage is defined as Vm =  V1 – V2 and the common mode input voltage is defined as These equation show that if  V1 = V2, then the differential mode input signal is zero and common mode input signal is Vcm =  V1 =V2.

## Differential Amplifier with Active load:

Differential amplifier is designed with active loads to increase the differential mode voltage gain. The open circuit voltage gain of an op-amp is needed to be as large as possible. This is got by cascading the gain stages which increase the phase shift and the amplifier also becomes vulnerable to oscillations. The gain can be increased by using large values of collector resistance. For such a circuit, the voltage gain is given by

To increase the gain the IC RC product must be made very large. However, there are limitations in IC fabrication such as,

1.        A large value of resistance needs a large chip area.

2.        For large RC, the quiescent drop across the resistor increase and a large power supply will be required to maintain a given operating current.

3.        Large monolithic resistor introduces large parasitic capacitances which limits the frequency response of the amplifier.

4.        for linear operation of the differential pair, the devices should not be allowed to enter into saturation. This limits the max input voltage that can be applied to the bases of transistors Q1 and Q2 the base-collector junction must be allowed to become forward-biased by more than 0.5V. The large value of load resistance produces a large dc voltage drop (IEE / 2) RC, so that the collector voltage will be VC=Vcc - (IEE/2) RC and it will be substantially less than the supply voltage Vcc. This will reduce the input voltage range of the differential amplifier. Due to the reasons cited above, an active load is preferred in the differential amplifier configurations.

### BJT Differential Amplifier using active loads:

A simple active load circuit for a differential amplifier is the current mirror active load as shown in figure. The active load comprises of transistors Q3 and Q4 with the transistor Q3 connected as a Diode with its base and collector shorted. The circuit is shown to drive a load RL. When an ac input voltage is applied to the differential amplifier, the various currents of the circuit are given by IC4 = IC3 = IC1 = gmVid/2 where IC4 = IC3 due to current mirror action.

IC2 = - gmVid/2 .

We know that the load current IL entering the next stage is IL= IC2-IC4 = - gmVid/2 - gmVid/2 = - gmVid

Then, the output voltage from the differential= amplifier= is given by V0= - ILRL = gm RLVid. The ac voltage gain of the circuit is given by Av = v0/vid = gmRL. The amplifier can amplify the differential input signals and it provides single-ended output with a ground reference since the load RL is connected to only one output terminal. This is made possible by the use of the current mirror active load. The output resistance R0 of the circuit is that offered by the parallel combination of transistors Q2 (NPN) and Q4 (PNP). It is given by Rr = r02 || r04. ### Analysis of BJT differential amplifier with active load:

The collector currents of all the transistors are equal.

IC1 = IC2 = IC3 =IC4 = IEE/2 .

The Collector -emitter voltages of Q1 and Q2 are given by

VCE1-VCE2 =VC-VE=VCC - VEB-(-VEB)= VCC

Eqn. shows that, the offset is higher than that of a resistive loaded differential amplifier A. This can be reduced by the use of emitter resistors for Q3 and Q4 , and a transistor Q5 in the current mirror load.

### CMRR of the differential amplifier using active load:

The differential amplifier using active load provides high voltage gain to the differential input signal and a single – ended output that is referenced to the ground is obtained. The differential amplifier which provides conversion for a differential signal to a single ended signal is necessary in differential input signal ended output amplifiers. The op-amp is one such circuit. The changes in the common-mode signal of the bias current source. This induces a change in IC2 and an identical change in IC1. The change in IC1 will then produce a change in the PNP load devices, and thereby a change in IC4, which is the collector current Q4, The current IC4 is in such a direction as to cancel the change in IC2. As a result of this, any common mode input does not cause a change in output.

The voltage gain of the differential amplifier is independent of the quiescent current IEE. This makes it possible to use very small value of IEE as low as 20μA, while still maintaining a large voltage gain. Small value of IEE is preferred, since it results in a small value of bias current and a large value for the input resistance. A limitation in choosing a small IEE is, however, the fact that, it will result in a poor frequency response of the amplifier. When a small value of bias current is required, the best approach is to use a JFET or MOSFET differential amplifier that is operated at comparatively higher values of IEE. ### Differential Mode signal analysis:

The ac analysis of the differential amplifier can be made using the circuit model as shown below. The differential input transistor pair produces equal and opposite currents whose amplitude us given by gm2 Vid /2 at the collector of Q1 and Q2. The collector current Ic1 is fed by the transistor Q3 and it is mirrored at the output of Q4. Therefore, the total current i0 flowing through the load resistor RL is given by i0 = [2gm2Vid]/2 = gm2Vid.

Then the output voltage is  v0 =i0RL – gm2RLvid and the differential mode gain Ad of the differential amplifier is This current mirror provides a single ended output which has a voltage equal to the maximum gain of the common emitter amplifier.

The power of the current mirror can be increased by including additional common collector stages at the o/p of the differential input stage. A bipolar differential amplifier structure with additional stages is shown in figure. The resistance at the output of the differential stage is now given by the parallel combination of transistors Q2 and Q4 and the input resistance is offered by Q5. Then, the equivalent resistance is expressed by Req = ro2 || r04 || ri5 = ri5.

The gain of the differential stage then becomes  Adm  = gm2 Req = gm2 ri5=βIC2/IC5 . Tags : explanation with block diagram | Operational Amplifiers , Linear Integrated Circuits : Basics of Operational Amplifiers
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Linear Integrated Circuits : Basics of Operational Amplifiers : Differential amplifier | explanation with block diagram | Operational Amplifiers