The CC-CE, CC-CC, and Darlington Configurations
The Darlington pair – CC-CC configuration
Let's consider the circuit of fig. 41, where the biasing components are omitted.
If we suppose that T1 º T2 and that they are equally biased, let's compute the voltage gain and input resistance:
that leads to
If b » 2, we have
and if gm RE >> 1, we may write the approximate value of Av:
which is the same expression we get for the single transistor emitter follower.
But the input resistance, if b >> 1 and RE >> 11/gm is:
much larger than the value b RE, that is the approximate value we get for a single transistor.
In the same way, the short-circuit current gain is (b +1)2 much larger than (b +1) that the single stage has.
Finally, the output resistance is the same in both cases (1/gm), if the first base is connected to ground.
Probably, the most interesting result is that the two transistor montage can be seen as one only transistor where the three terminals (B, C, E) are respectively, the first base, both collectors and the second emitter and displays a large current gain, typically b 2. However, this is not completely true because in general the two transistors are very different being common that the first is a high b small signal transistor while the second is a low b power transistor.
We may conclude that this circuit has approximately the same voltage gain as a simple CE, but a much larger input resistance (
b times larger). However, as the internal ouput resistance is halved (ro / 2), the maximum possible gain is smaller than what we can get with one only transistor.
Therefore, this circuit has the required characteristics for the intermediate stage of an OpAmp. However, the high frequency response is deficient. In fact, Cm of T1 is subject to a very strong Miller effect.
Common Emitter Darlington configuration
In spite of what has just been said, we will admit, for the sake of simplicity, that both transistors have the same characteristics and biasing point. Then, let's consider the schematic of fig. 42.
Input resistance:
Voltage gain:
and
We may conclude that this circuit has approximately the same voltage gain as a simple CE, but a much larger input resistance (b times larger).
However, as the internal ouput resistance is halved (ro / 2), the maximum possible gain is smaller than what we can get with one only transistor.
Therefore, this circuit has the required characteristics for the intermediate stage of an OpAmp. However, the high frequency response is deficient. In fact, Cm of T1 is subject to a very strong Miller effect.
CC-CE configuration
Fig. 43 represents the CC-CE circuit and its small signal equivalent. This is very similar to the circuit we just analysed (the Darlington montage) except for the fact that the two collectors are not connected.
fig. 43 - CC-EC configuration; (a) simplified schematic; (b) small signal equivalent circuit
Voltage gain:
and
Again, for the sake of simplicity, we will admit that T1 and T2 are equal and equally biased.
Input resistance:
This circuit presents the same gain and input resistance as the CE Darlington transistor. However the maximum voltage gain is twice as large, since the output resistance (ro) is doubled.
Though, the most significant change concerns the bandwidth. As the first stage (CE) has a good high frequency response, as we have seen before, and the Miller effect upon Cm of the second transistor does not limit much since it is charged by the low output resistance of the emitter follower the frequency behaviour of the circuit is quite good.
This is why this montage is quite common in the intermediate stage of general purpose OpAmps.
We have been referring to the common configurations of general purpose OpAmps. In general they still have a last stage that should satisfy two requirements: to have a high input resistance not to degrade the voltage gain of previous stages and have a low output resistance to be able to drive the output load. The voltage gain does not need to be high, since the two previous stages are able to provide it. Therefore, these are the characteristics we expect to find in an emitter follower circuit.
Rooselvet Ramirez EES
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