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AE_Lecture7_Multistage Amplifier

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_Lecture7 describes the different kinds of multistage amplifiers and the effect of cascading on different performance parameters especially on BW.

AE_LECTURE7_ MULTISTAGE AMPLIFIERS

In real world, a variety of combination of performance specifications have to be achieved.

One such combination as required for an op-amp is:

Figure 1
Figure 1 (graphics1.png)

This cannot be met by a single stage amplifier. By cascading several stages we achieve it .

Figure 2
Figure 2 (Picture 1.png)

Figure 1. Block Diagram of an Op Amp which is a cascaded amplifier.

While designing multi-stage amplifier, if we have capacitance coupling then it becomes easier to design since there is no DC interaction.

But in a directly coupled multistage amplifier since we have DC interaction hence it is difficult to design.

A direct coupled amplifier implies DC Amplifier whereas a capacitive coupled amplifier implies AC Amplifier as RC-coupled Amplifier is.

COMMONLY USED CASCADED AMPLIFIER

Figure 3
Figure 3 (Picture 2.png)

Figure 3. The Block Diagram of commonly used Cascaded Amplifier.

Figure 4
Figure 4 (Picture 3.png)
v

Figure 3. Actual implementation of Instrumentation Amplifier using a cascade of CS-CE-CC.

Figure 5
Figure 5 (Picture 5.png)

Figure 4. EQUIVALENT CIRCUIT of the above cascade at MID FREQUENCY.

In Multi-stage amplifiers we have the problem of BAND WIDTH SHRINKAGE.

In Figure 5, the Bode Plot of single stage amplifier is shown. As can be seen the frequency response is that of Band-Pass filter with lower -3dB frequency being fL and upper -3dB being fH . The skirt of the response is -20dB/decade at the higher end and +20dB/decade at lower end. The mid-band gain or flat band-gain is 20dB.

If two such identical Amplifiers are cascaded in a non-interacting fashion then overall gain will be +40dB but the BW will shrink as shown in Figure 6. The skirts are steeper: 40dB/decade at lower end and -4-dB/decade at higher end. The upper cut-off frequency now is

fH = fH′×Sn where Sn=shrinkage factor and fL = fL′/Sn as shown in Figure 6.

Figure 6
Figure 6 (Picture 7.png)
Figure 7
Figure 7 (Picture 8.png)

From Figure 6 it is clear that single stage amplifier has a mid-band gain of 20dB and -3dB BW of

[f ′ H – f ′L] whereas a double stage amplifier has a mid-band gain of 40 dB and -3dB BW is [fH-fL] where [fH-fL] = f 'H× S2 – f 'L/ S2 and S2 = √(21/2-1) = 0.64= shrinkage factor of a double stage amplifier.

Figure 8
Figure 8 (graphics2.png)

For n stage cascade of identical amplifiers

Figure 9
Figure 9 (graphics3.png)
Figure 10
Figure 10 (graphics4.png)

Where fL = lower -3dB frequency of single stage and fH = Upper -3dB frequency of single stage amplifier.

Table 1
n 1 2 3 4 5
graphics5.png 1 0.64 0.51 0.44 0.34

This formula is applicable only if there are identical stages which we cascade in a non interacting manner.

Figure 11
Figure 11 (Picture 9.png)

If these identical stages are cascaded without buffer then they will interact among themselves and even if they are identical their individual upper -3dB frequencies and lower -3dB frequencies will get dispersed and there are non-identical upper -3dB frequencies

Figure 12
Figure 12 (graphics6.png)
.

Then the overall upper -3dB frequency

Figure 13
Figure 13 (graphics7.png)
,

Figure 14
Figure 14 (graphics8.png)

This equation implies that in time domain the overall rise time

Figure 15
Figure 15 (graphics9.png)

In case of lower -3dB frequencies, the individual lower -3dB frequencies are

Figure 16
Figure 16 (graphics10.png)
and in that case the overall -3dB frequency is given by the following formula:

Figure 17
Figure 17 (graphics11.png)

This formula implies that overall sag=

Figure 18
Figure 18 (graphics12.png)

Therefore for obtaining 10% sag we will have to increase the frequency

Figure 19
Figure 19 (graphics13.png)

Hence

Figure 20
Figure 20 (graphics14.png)
will also increase.

In identical stages with non-interacting cascade shrinkage factor will decide the band-width whereas in interacting cascade the above equations will decide the band-width.

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