**Darlington Amplifier – Circuit Diagram, Characteristics, Merits and Applications:**

Darlington amplifier with voltage divider bias is shown in Fig. 19.50. In this circuit the output of one amplifier is coupled into the input of the next one by directly joining emitter of one transistor to the base of the other one, as shown in the figure. Obviously, the emitter current of the first transistor becomes the base current for the second transistor.

The biasing analysis is similar to that for one transistor except that two V_{BE} drops are to be considered.

The Darlington amplifier circuit in its small signal ac form will appear, as shown in Fig. 19.51.

**Main Characteristics:**

**1. Current Gain:** For the second stage:

Input impedance,

and current gain,

On a good approximate basis, these equations cannot be applied to the first stage. The “fly in the ointment” is the closeness with which Z_{in2} compares with 1/h_{oe1}. We have seen that 1/h_{oe}, could be eliminated in the majority of the cases because the load impedance Z_{L}Â << 1/h_{oe}. For the Darlington Amplifier circuit the input impedance Z_{in2} is close enough in magnitude to 1/h_{oe }toÂ necessitate considering the effects of h_{oe1}. We already discussed that, it was found that for single stage grounded emitter transistor amplifier, where 1/h_{oe} was considered,

Applying the above equation to this situation,

and current gain,

Current gain,

For h_{oe}h_{fe}R_{E}Â â‰¤ 0.1,Â a fairly good approximation (within 10%) is

Alternatively current gain can be obtained as follows:

Emitter current,

So current gain,

It means Darlington amplifier behaves like a single transistor having current gain equal to Î²^{2}.

**2. Input Impedance:** Since Z_{in2}Â = h_{fe2}R_{E}Â is the emitter resistance of the first stage, the input impedance to the first stage is

Since Z_{in2}Â = h_{fe2}R_{E}, and 1/h_{oe1} will appear in parallel in the small signal equivalent circuit, so

Alternatively input impedance can be obtained as follows:

Input impedance of second stage,

where râ€²_{e2} is the ac emitter resistance of second transistor.

If R_{E}Â >> râ€²_{e2}, then Z_{in2}Â = Î²_{2}R_{E}

Z_{in2} is also the output impedance while looking into the emitter of first transistor. So input impedance looking into the base of first transistor,

This input impedance is very high because of the product of two betas,

so input impedance,

If there is a load resistance R_{L} coupled to the emitter of second transistor, then

**3. Output Impedance:** The output impedance Z_{out} can be determined directly from the emitter equivalent circuits as follows:

Alternatively the output impedance Z_{out} can be determined as follows :

The ac Thevenin’s impedance at the input r_{Th}Â = R_{s}||R_{1}||R_{2}Â because by shorting all voltage sources R_{1} and R_{s} comes in parallel with R_{2}

Output impedance of first stage,

Output impedance of second stage,

Z_{out2} is quiet smaller than Z_{out1}Â i.e., output impedance is lowered.

Because of this, Darlington amplifier can be used to isolate high impedance source from low impedance load. If high impedance source is directly connected to a low impedance load, most of the signal voltage will be dropped across the high impedance of the source and remaining source signal available may not be able to drive the load.

**4. Voltage Gain:** Applying Kirchhoff’s voltage law to the circuit shown in Fig. 19.50.

That the output potential is the input potential less the base-Âto-emitter potential of each transistor. It clearly indicates that V_{out}Â < V_{in}. Voltage gain is closer in magnitude to one than to zero.

On an approximate basis it is given as

On an approximate basis voltage gain can be determined from the following relation also

(slightly less than unity) as in case of emitter follower

**Note :** râ€²_{e1}Â and râ€²_{e2} have been assumed to be equal and each one equal to râ€²_{e}.

**Merits:**

- It uses very few components and can be readily formed from two adjacent transistors in an IC.
- It provides excellent characteristics of high input impedance with low output impedance and high current gain, all desirable characteristics for a current gain amplifier.

**Applications of Darlington Amplifier:**

It has enormous impedance transformation capability i.e., it can transform a low impedance load to a high impedance load. Hence it is used in a high gain operational amplifier which depends on very high input impedance for its operation as an integrator or summing amplifier in analogue applications.