94	Analysis and Application of Analog Electronic Circuits

effect for the upper (G-B) BJT and the Miller effect for the lower (G-E) BJT is very small because the Ve/Vs voltage gain magnitude is <1. Namely,

Ve	(0) =	−gmrπ (1+ gmrπ )		= −0.8877	(2.176)
V
		1+ R	s
s		s	π

In summary, certain oneand two-transistor amplifier designs are inherently broadband because they avoid the Miller effect. These designs include the emitter-follower; grounded-base; source-follower; grounded-gate; EF–GB pair; and cascode amplifiers. The next section examines some other schemes for increasing high-frequency response, also known as broadbanding. One way is to trade-off mid-band gain for high-frequency bandwidth by using negative feedback. Another is to use a high-pass zero to cancel a low-pass pole, effectively extending high-frequency bandwidth. Still another is to ensure that the Thevenin source resistance of the first stage’s output is very low compared to the input resistance of the second stage; an emitter follower is often used to realize low Rs1.

2.5.5Broadbanding Strategies

In op amps, instrumentation amplifiers, and other IC amplifiers, multiple transistor stages are used to achieve the requisite gain. The gain stages are generally direct coupled (DC), i.e., there is a dc pathway from the output of one stage to the input of the next gain stage. Thus DC amplifiers can amplify dc signals. To match appropriate dc bias voltages between the output of one stage and the input of the following stage, often a resistive voltage divider is used. Another strategy to match dc levels is to alternate pnp and npn BJTs in the stages (or p-channel and n-channel FETs). An advantage of the voltage divider is that it allows one to use shunt capacitive frequency compensation.

Figure 2.53 illustrates two stages of a DC amplifier in general format; the first stage is represented by a frequency-independent Thevenin model, coupled to the input of the second stage through a voltage divider, (R1, R2). The input resistance and capacitance of the second stage are Ri, Ci, respectively. V2 drives the second stage. The shunt capacitor, C1, can be used to cancel the low-pass effect of the input capacitance. To illustrate this effect, find the transfer function, V2/V1, using the simple voltage-divider relation:

				1
V2	(s) =			Gin + sCi						(2.177)
V1			1				1
					+ Rs1	+
							G1 + sC1
			Gin + sCi

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Models for Semiconductor Devices Used in Analog Electronic Systems				95
	C1
Rs1	R1
+			+
V1	R2 Ri	Ci	V2
−	−

FIGURE 2.53

An R–C voltage divider model for direct coupling between amplifier stages. It is shown that a nearly flat frequency response occurs when R1C1 = Ci (Ri R2).

where:

	Rin	=		1	= 1 Gm	(2.178)
			G2	+ Gi

Adjust C1 so that C1R1 = CiRin and do algebra to find:

				Rin
V2	(s) =		Rin + R1 + Rs1				(2.179)
V1
		1+		sCiRs1Rin
				Rin + R1 + Rs1

Note that, if Rs1 0, V2/V1 Rin/(Rin + R1) (V2/V1 is independent of frequency); otherwise the break frequency is quite high.

Another general principle of extending the high-frequency bandwidth of a multistage, inverting-gain amplifier is to trade-off mid-band gain for bandwidth through the use of negative feedback. The classic illustration of the gain-bandwidth constancy is done with op amps in Section 6.3 in Chapter 6. A similar example will be examined here; see Figure 2.54 for the circuit. Without feedback (RF = •), an inspection shows that the amplifier’s frequency response is:

	V		−μ
	o	(jω) =				(2.180)
	V		1+ jωτ	a
	s
The gain-bandwidth product of this amplifier without feedback is:
GBWPo = μ/τa r/s						(2.181)

© 2004 by CRC Press LLC

96	Analysis and Application of Analog Electronic Circuits

RF

	Rs			+
	Vi	−
	+	µ
			Vi	Vo
	Vs	τa s + 1
		+
				−
	−

FIGURE 2.54

Circuit illustrating the trade-off of gain for bandwidth using negative feedback. See text for analysis.

With feedback, Vi is given by the node equation:
				Vi[Gs + GF ]− VoGF = VsGs							(2.182A)
						¬
	−	sτ	a		+ 1 V
(					)	o	[Gs + GF ]− VoGF = VsGs				(2.182B)
				μ
						¬
		V			(s) =	−RF μ [RF + Rs (1+ μ)]					(2.182C)
		o						sτa (RF	+ Rs )
		Vs
								[RF + Rs	(1+ μ)]

The gain-bandwidth product with feedback is:

GBWPf = μ [τa (1+ Rs RF )]

(2.183)

Assuming that μ 1 and μRs RF yields the approximate frequency

response function:
	V			−R	R
	o	(jω)		F	s			(2.184)
	V			jωτa
	s			μRs (Rs + RF ) + 1

© 2004 by CRC Press LLC