When lite It,ilcctors 01 two OJ tied together and the ernittor of one is directcoupled to the base of the other, as shown in Figure 11-1 X, we obtain ct. imponant and highly usciul ~()l1figar;lI;ol ca!h.l; Darlington pair, The com hi nation is used ill amplitin circuits as if it were a single transistor having the base, collector, and emitter terminals labeled B, C, and E in the llyze the Darlington pair to discover the effective beta (f3IJI’) of the single transistor it represents, as well as some of its small-signal characteristics.

Let f31 and f32 be the de f3-values of 01 and O!, respectively, Then, hy definition,

Equation 11-24 shows that the effective {3 of the Darlington pair is the product plus the sum of the {3’s of the individual transistors. It is usually true that {31{32» {31+ {31, S}

Darlington pairs arc often tabricatcd on a single chip tl\ achieve matched 01 and O! characteristics. WI en {31== /3l == {3,we have an effective f3 1)

Darlington pair can he regarded as a “super-{3” transistor, and therefore enjoys all the advantagl!s that high-{3 transistors have. For example, the de resistance looking into the base (of 01) is the very large value {3m·Rf:, where Rc is the resistance between the emitter (of Or) and ground.

While the foregoing analysis was performed for de currents and t rc de {3-values, a’l identical small- signal analysis sho vs that the small-signal value of {31l1i’s the product plus the sum of the small-signal values of {31and {32′ Hereafter we will make the usual assumption that the de and small-signal values of (3 are approximately equal and will not distinguish between the two.

We wish now to determine the effective small-signal input esistance from B to E, ‘”,(1m, and the emitter resistance, ,,~()/,),of the composite transistor. Recall the general relationship (equation 5-22):

The total effective resistance looking into the bast! of 01 (across the composite B-E terminals), i.c., the effective small-signal input resistance of the Darlington pair, is

A Darlington pair is biased so. that the total collector current is 2 mA. If {31= 110 and (3~= 100, find the room-temperature values

‘111isexample shows that the Darlington pair can be used to obtain a signilicant increase in base-to-emitter input resistance.

The Darlington pair is most often used in an emitter-follower configuration because of the excellent buffering it provides between a high-impedance source and a low-impedance load. With an ac load resistance ‘I.connected to the emitter, the total input resistance to the follower is

When operated as ‘an emitter follower, the current gain the base of 01 to the ” emitter of O! is Ai == i,2/ihl’ Since i,’1 = i,,!, we have The next example illustrates an ext rcmc case of t he need for buffering, where the source resistance.

Without till: hullering provided by the Darlington pair, the output voltage turns out to be less than half the level of the input signal, i.c., we no longer have a voltage amplifier. We see that the Darlington pair increases the voltage gain by a factor of 41.3/0.22 = IX7.7

**Cascode Amplifier**

Another important ex ample of direct-coupled trunsistor» is the casco.!« amplifier (a name derived from vacuum-tube days), in which a common-cmiucr transistor drives a common-base transistor. A simple example of a cascode amplifier Iote that 01 is a common-emitter stage that uses Rill for “fixed” bias. Since capacitor ell grounds the base of 02 to ac signals, 02 is the commonbase stage. It serves as the load on the collector of 01. Recall that the input to a common-base stage is at its emitter and the output is taken at its collector. Thus 01 is direct-coupled to the input of 02 and the output of the eascode amplifier is at the collector of 02. Resistors RI and Rz form a voltage-divider bias circuit for 02, The principal advantage of the casco de arrangement is that it has a small input capacitance, an important consideration in high-frequency amplifiers. The input capacitance is small because the voltage gain of 01 is small (near unity), which means that the Miller capacitance is minimized. Most of the voltage gain is achieved in the common-base stage. The voltage gain of 01 is small because the effective load resistance in its collector circuit is the small input resistance of the commonbase stage.

**IMG**

01, like any other comruou-cmitter stage, can also be biased using the voltagedivider method and all e-mitter resistor.

1 small signal equivalent circuit of the cascode amplifier. The collector. basco and emitter terminals of each transistor arc labeled in the diagram.

Note that the input resistance of is the small emitter resistance r.. of the commonbase stage. The parallel combination of rd/{31 and r•.! form the ac load on the collector of 01′ Since.

Equation 11-47 states that the voltage gain of 01 is approximately unity, which follows from the fact that, making 1′,’2 “” r”I’ The ac load on the collector of O2 is seen.

Find approximate values for

1. the de currents and voltages In, In, Vel> and VC2;

2. the small-signal voltage gain u,jus; and

3. the break frequency h.( ell) due to shunt capacitance at the input of 01.

**Solution**

1. The base-to-ground bias voltage at the input stage (01) is determined by the voltage-divider there. Since the voltage divider is loaded by {3Rf:l = 100 kO.

We see that the break frequency due to input capacitance is quite high. While there may be break frequencies elsewhere in ‘the circuit that lire smaller than 96 MHz (including the iil value of QI), the cascodc amplifier effectively eliminates the most troublesome source of high-frequency loss-the input Miller capacitance.