Also, we have already shown that the double-ended (difference) voltage ga:n equals the transistor gain and that the singlc-enocd output gain is one-half that value. Therefore, we conclude that We should note that these gain relations are valid irrespective of the magnitudes and phase relations of the two inputs Vii and Vi~’ We have considered only the two special cases where Vii and Vi2 are equal and in phase and where they are equal and out of phase, but equations 12-5 and 12-6 hold under any circumstances. Note also that VI’I and V,,2 will always have the same amplitude and be out of phase with each other. Thus,
The small-signal differential input resistance is defined to he the input difference voltage divided by the total input current. Imagine a signal source connected the input terminals, so the same current that flows out of the source into one input of the amplifier flows out of the other input and returns to the source. The signalsource voltage, whieh is the input difference voltage, divided by the signal-source current, is the differential input resistance. Since the total small-signal resistance :n the pnth from one input through both emitters to the other input is 21′,., the dilfcrcnual Input resistance.
the dc voltages and currents in the ideal differential amplitier. Since the transistors arc identical, the source current I divides equally between \ilem, and the emitter current in each is, therefore
For the ideal differential amplifier shown in Figure 12-11, find
1. the de output voltages V”I and’V,,2;
2. the single-ended output gain v”l/(vjl – V,’.!); and
3. the double-ended gain (U”I – v,,2)/(Vii – va).
The FET Differential Amplifier
Many differential amplifiers arc constructed using field-effect transistors because of the large impedance they present to input signals. This property is exceptionally important in many applications, including operational amplifiers, instrument amplifiers. and charge amplifiers. A large voltage gain is also important in these applications. and although the FET docs not produce much gain, an FET differential amplifier is often the first stage in a multistage amplifier whose overall gain is large.
Because FETs are easily fabricated in integrated-circuit form, PET differential amplifiers are commonly found in linear integrated circuits. Figure 12-12 shows a JFET differential amplifier. and it can be seen that it is basically the same configuration as its BJT counterpart. The two J FETs operate as common-source amplifiers with their source terminals joined. A constant-current source provides bias current.
The derivations of the gain equations for the J PET amplifier arc completely parallel to those for the BJT version. A source-to-ground voltage is developed ill the common source connection by source-follower action. Will- one input grounded, the output resistance and load resistance .,!the source follower are both equal to JIg,.. (assuming matched devices), so the source-follower gain is 0.5. Therefore. as shown in Figure 12-13, one-half the input voltage is developed across and the current.
Like the gain equations for the BJT differential amplifier, equations 12-14 and J 2-15 show that the double-ended (difference) voltage gain is the same as the gain of one transistor, and the single-ended output gain is one-half that value.