# Frequency Response of Cascaded Stages Electronics Help

In Chapter 10. we  i<:cussed the fact that the lower cutoff frequency of a single amplifier stage is influenced by as many as three different break I'<!qllencies. having v-ilues that depend on various RC components in the circuit. If the break frequencies were not close in value, VIe approxin., ~ d the actual lower cutoff frequency of the amplifier by assuming it to equal the largest of those break frequencies. Similarly. Have assumed the upper cutoff frequency to be the smatresi u he break trcquencie . that affect the high-frequency response. The same reasoning applies to ascadcd amplifier stages. If the lower cutoff frequencies of the individual stages arc not close in value, the overall lower cutoff frequency is approximately equal to the largest of the stage lower cutoff frequencies. If the upper  of the individual stages arc not close in value, the overall upper cutoff frequency is approximately equal to the smallest of the stage upper cutoff frequencies. In practice, a multistage amplifier may have some lower break frequencies that are equal, or close in value. and others that are not. The same is true for upper break frequencies. In these situations, computation of the actual lower and upper cutoff frequencies of a multistage amplifier is a very complex problem, From a practical standpoint. the cutoff frequencies are best determined experimentally or by use of a computer program that computes the overall frequency response,

For the special cases where all stages of a multistage amplifier have identical lower cutoff frequencies or identical upper cutoff frequencies, the overall cutoff frequencies can be calculated readily:

values of/) in) terms of j; and I!. for II ranging from I to 5. Note that when n = 2, /)(‘R'<rall) = 1.55j; and /2(<1<‘<1011) = in agreement with our discussion in Chapter 10 for the case of two identical break frequencies in a single stage. The table confirms what should be intuitively clear: the greater the number of identical stages, the larger the lower cutoff frequency and the smaller the upper cutof] frequency. In other words, the act of cascading stage with identical frequency-response characteristics reduces the overall bandwidth of a multistage amplifier. When 11 stages having identical frequency response arc cascaded, the overall frequency response falls off along asymptotes having slopes 2011 decade (6/1 dB/octave) at frequencies outside the midband range. The break frequencies are in all cases equal to the cutoff frequencies of a single stage

METHODS OF COUPLING

The circuitry used to connect the output of one stage of a multistage amplifier to the input of the next stage is called the coupling method. In previous chapters, we have discussed only one such method: capacitor coupling, also called RC coupling because the interstage circuitry is equivalent to a high-pass RC network. In this chapter we will consider two additional coupling methods: direct coupling and transjonncr coupling.

Recall that the primary reason for employing RC coupling is to block the flow of de current. We have observed that it is often necessary to prevent _the flow de current between the input of an amplifier and its signal source, as well as between the amplifier’s output and its load. Similarly, RC coupling is used to prevent decurrent from flowing between the output of one amplifier stage and the input of the next stage. The capacitor connected in the path between amplifier stages makes it possible to have a de bias voltage at the output of one stage that is different from the de bias voltage at the input to the next stage. This idea is illustrated 11-5, which shows the output of a BJT amplifier stage connected through a coupling capacitor to the input of another BJT amplifier stage. Notice that the collector of the first stage is at +9 V and that the base of the second stage is at +3 V. The  voltage across the capacitor is therefore 9 – 3 = 6 V, <::0 the capacitor should have a de-working-voltage (DCWV) rating somewhat greater than 6 v. If the lO-J,F coupling capacitor is of the electrolytic type, it must be connected with its positive terminal to the more positive bias voltage: the 9-V collector voltage in this example.

Of course, a coupling capacitor permits the flow of {If’ sio nal current between stages, provided the frequency is high enough to keep the capacitive reactance small. The disadvantage of the RC coupling method is that it affects the lowfrequency response of the amplifier; we must sometimes.choose between an impractically large capacitor value and an unreasonably large lower cutoff frequency. RC coupling is not used in integrated circuits because it is difficult and uneconomical to fabricate capacitors on a chip.

As the name implies, direct couplingis the coupling method in which the output of one stage is electrically connected directly to the input of the next stage. In other words, both the de and ac voltages at the output of one stage are identical to those at the input of the next stage. The method is often referred to as de, which, in the context of signal coupling, means both direct coupling and direct current. Clearly, any change in the de voltage at the output of one stage produces an identical change in dc voltage at the input to the next stage, so a direct-coupled amplifier behaves like a direct-current amplifier. Direct coupling is used in differential and operational amplifiers, which we will study extensively in Chapter 12. and in integrated circuits.

We will investigate some examples of direct-coupled discrete amplifiers later in the present chapter.Another method of coupling an ac signal from one stage to another while maintaining de isolation hetween them is through the use of a transformer. The primary winding of the transformer is in the output circuit of one stage and the secondary winding is in the input circuit of the following stage. In this way. the ac signal is passed from one stage to the next without the possibility of de current flowing between the two. The advantages of transformer coupling include low dc power dissipation and the capability for designing a turns ratio that results iil maximum power transfer between stages. We will investigate how this is accomplished in an illustrative example using hipolar transistors. The disadvantages of transformer coupling include the bulk and cost of the transformers themselves and their generally poor frequency-response characteristics. The transformer inductance and interwinding capacitance tend to reduce the usable bandwidth of these amplifiers.However, they arc often used in narrow band applications, such as radiofrequency (rf) amplifiers.

Posted on November 18, 2015 in MULTISTAGE AMPLIFIES