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VAAGDEVI INSTITUTE OF TECHNOLOGY & SCIENCE
ANALOG CIRCUITS
UNIT- 1 Multistage and Differential Amplifiers
Syllabus:
๏ Introduction โ Recap of Small Signal Amplifiers
๏ Multistage Amplifiers, Cascode amplifier
๏ Darlington pair
๏ the MOS Differential Pair
๏ Small-Signal Operation of the MOS Differential Pair
๏ The BJT Differential Pair
๏ Nonideal Characteristics of the Differential Amplifier.
AMPLIFIER:
A circuit that increases amplitude of given signal is an amplifier. The amplifier is an electronic circuit, which amplifies or increases strength of weak signal.
๏ A small AC signal fed into amplifier is obtained as large AC signal of same frequency. ๏ A amplifier is essential part in radios, TVโs and other communications A linear amplifier magnifies an input signal and produces an output signal whose magnitude is larger and directly proportional to the input signal.
The ac analysis, called a small-signal analysis, can be performed with the dc source set to zero.
Small-Signal Hybrid-ฯ Equivalent Circuit of the Bipolar Transistor
All the transistor amplifiers are two port networks having two voltages and two currents. The positive directions of voltages and currents.Out of four variables two can be selected as are independent variables and two are dependent variables.
In h- parameters
๏ (V 1 & I 2 ) โ Dependent Variables ๏ (I 1 & V 2 ) โ Independent Variables
Assuming the transistor as two port network. The iB vs vBE graph the small time varying signal is superimposed on Q-point. The slope of Q-point is constant with units of conductance.
Substitute equation 2 in 1
We can then write the small-signal collector current as ๐๐ = ๐๐๐ฝ๐๐
By using above equation we have to draw output port
Combine input port an output port, we will get small signal Hybrid-ฯ Equivalent Circuit of the Bipolar Transistor
Fig: A simplified small-signal hybrid- ฯ equivalent circuit
Alternative Form of Equivalent Circuit
๐๐ถ = (^) ๐ ๐๐ ๐๐ถ๐ต |๐โ๐๐ก. ๐๐ต
๐คโ๐๐๐ ๐ ๐ ๐ ๐๐ถ๐ต |๐โ๐๐ก โก ๐ฝ
We can then write as ๐๐ = ๐ท ๐๐
๐๐
๐๐ = [๐ท๐ฝ ๐ฐ๐ช๐ธ๐ป ] [๐ฐ ๐ฝ๐ช๐ธ๐ป ] = ๐ท
Small-Signal Equivalent-Circuit Models:
Fig. MOSFET ๏ The FET behaves as a voltage-controlled current source. ๏ It accepts a signal vgs between gate and source and provides a current gmvgs at the drain terminal. ๏ The input resistance of this controlled source is very high and ideally infinite. ๏ The output resistance looking into the drain also is high, and we have assumed it to be infinite. The DC bias current is ๐ผ๐ท = 12 ๐๐โฒ ๐๐ฟ (๐๐๐ โ ๐๐ก)^2 ๐๐โฒ^ = ๐๐๐ถ๐๐ VOV = VGS - Vt is the overdrive voltage at which the MOSFET is biased to operate. ๐๐ = ๐๐โฒ ๐๐ฟ (๐๐๐ โ ๐๐ก) = ๐๐โฒ ๐๐ฟ ๐๐๐
๐๐ = (^) ๐๐๐ 2 ๐ผโ๐๐ท๐ก = 2 ๐ผ ๐๐๐๐ท
The small-signal model of the MOSFET
๐๐๐ฝ๐
๐
1 || ๐
2 ||๐๐
๐๐ = โ๐๐๐๐[๐๐||๐
๐ถ ] ---
And the control voltage ๐๐ is found to be
๐๐ = (๐
1 ๐
||๐
^1 ||๐
2 ||๐^2 ||๐๐)+๐
๐ ๐ . ๐๐ ---
Substitute eq2 in eq
๐๐ = โ๐๐ (๐
1 ๐
||๐
^1 ||๐
2 ||๐^2 ||๐๐)+๐
๐ ๐ . ๐๐ [๐๐||๐
๐ถ ]
๐จ๐ฝ = ๐ฝ ๐ฝ๐ถ๐บ = โ๐๐ [๐๐||๐น๐ช] [ (๐น๐น๐||๐น๐||๐๐
๐||๐น๐||๐๐
)^ + ๐น๐
]
Assume ๐
1 ||๐
2 ||๐๐ = ๐
๐ต and ๐๐||๐
๐ถ = ๐
๐ถ
Multistage amplifiers:
๏ In practical applications, the output of a single state amplifier is usually
insufficient, though it is a voltage or power amplifier. Hence they are replaced
by Multistage amplifiers.
๏ A generalized three-stage amplifier is shown in below figure.
Fig. A generalized three-stage amplifier
๏ In Multi-stage amplifiers, the output of first stage is coupled to the input of next
stage using a coupling device. These coupling devices can usually be a
capacitor or a transformer. This process of joining two amplifier stages using a
coupling device can be called as Cascading.
๏ In general, the input impedance of the first stage must be high and the output
impedance of the last must be low.
๏ The overall gain is the product of the individual gains.
Cascode Amplifier :
๏ Cascode amplifier is a type of multistage amplifier. The CE amplifier followed by CB amplifier is called cascode amplifier. The high bandwidth and high gain are major advantages of cascode amplifier. The input is into a common-emitter amplifier (Q 1 ), which drives a common-base amplifier (Q 2 ). The output signal current of Q 1 is the input signal of Q 2.
Fig. Cascode amplifier
F
i g
. Small-signal equivalent circuit of the cascode amplifier
The bias resistance of the amplifier is ๐น๐ฉ๐ = ๐น๐ โฅ ๐น๐
The input resistance of the amplifier is ๐น๐ = ๐น๐ฉ๐ โฅ ๐๐
๐ The out resistance of the amplifier is ๐น๐ = ๐น๐ช Vฯ1 = Vs since we are assuming an ideal signal voltage source.
The Voltage gain of the amplifier is
The output voltage is ๐๐ = โ๐๐2๐๐2[๐
๐ โฅ ๐น๐ณ]^ --- Writing a KCL equation at E 2 , we have ๐๐1๐๐1 = ๐ ๐๐2๐2 + ๐๐2๐๐ The control voltage V ฯ2 (noting that Vฯ1 = Vs ), we find ๐๐2 = ๐๐1๐๐ ๐๐2 โ ๐๐2๐๐2 ๐๐ ๐๐2 + ๐๐2๐๐2 ๐๐2 = ๐๐1๐๐ ๐๐ ๐๐2(1 + ๐๐2 ๐๐2) = ๐๐1๐๐ ๐๐ ๐๐2 = (^) (1+๐๐๐1๐2๐๐ ๐ ๐2๐๐2) โด ๐ฝ 2 = ๐๐2 ๐๐
๐๐2 = ( (^) 1+๐ฝ๐๐2 2 ) ๐๐1๐๐ --- Substitute eq. (3) in eq. (2), we get output voltage as ๐๐ = โ๐๐1๐๐2 ( (^) 1+๐ฝ๐๐2 2 ) ๐๐1๐๐ [๐
๐ โฅ ๐น๐ณ] Therefore, the small-signal voltage gain is
๐จ๐๐ = ๐ฝ ๐ฝ๐๐ = โ๐๐๐๐๐๐ ( ๐+๐ท๐๐
๐๐ ) ๐๐๐ [๐น๐ โฅ ๐น๐ณ]
We know that ๐๐2 ( (^) 1+๐ฝ๐๐2 2 ) = (^) 1+๐ฝ๐ฝ^22 โ
1 The gain of the cascode amplifier is then approximately
๐จ๐๐ โ
= โ๐๐๐ [๐น๐ โฅ ๐น๐ณ]
Which is the same as for a single-stage common-emitter amplifier.
The current gain of the amplifier is ๐จ๐ฐ๐บ = ๐ฐ ๐ฐ๐ถ๐
๏ The overall current gain of darrlington pair is multiplication of individual current gains. ๏ง If matched transistors then ฮฒ1=ฮฒ2 then ฮฒd=๐ฝ1^2
๏ Generally darlington pair available in package contain 3 terminals i.e. base ,emitter ,and collector ๏ Darlington pair can be used as emitter follower its equivalent is cascading of two emitter followers.
Fig: A Darlington pair amplifier or configuration The Darlington pair basically consisting of two bipolar transistors with the emitter of one transistor connected to the base of the other, such that the current amplified by the first transistor is amplified further by the second one.
The collectors of both transistors are connected together. It is often packaged as a single transistor. The high current gain and high input impedance are the advantages of Darlington pair. One drawback is doubling of the baseโemitter voltage.
Fig: Small-signal equivalent circuit of Darlington pair ๐๐ธ1 = ๐๐1 + ๐ฝ 1 ๐๐1 = ๐๐1[1 + ๐ฝ 1 ] = ๐๐2 --- ๐๐ธ2 = ๐๐2 + ๐ฝ 1 ๐๐2 = ๐๐2[1 + ๐ฝ 2 ]^ --- Substitute equation 1 in 2 ๐๐ธ2 = ๐๐2[1 + ๐ฝ 2 ] = ๐๐1[1 + ๐ฝ 1 ][1 + ๐ฝ 2 ]^ --- Current gain
AI = ๐ ๐๐ธ2๐1 = ๐๐1[1+๐ฝ๐^1 ๐1][1+๐ฝ^2 ]
AI = [1 + ๐ฝ 1 ][1 + ๐ฝ 2 ]^ โด ๐ฝ 1 โซ 1, ๐ฝ 2 โซ 1 AI = ๐ฝ 1 ๐ฝ 2 โด identical transistors ๐ฝ 1 = ๐ฝ 2
๐๐ = ๐ท๐๐^ = ๐ท๐๐^ = ๐ท๐ซ
Voltage gain
๐ด๐ = ๐ ๐๐๐ = ๐๐ธ2 ๐๐
๐๐ธ = ๐๐1[1+๐ฝ^1 ][1+๐ฝ ๐๐^2 ] ๐
๐ธ ---
Apply KVL for input loop
๐๐ = ๐๐1 ๐๐1 + ๐๐2 ๐๐2 + ๐๐ธ2๐
๐ธ ---
Equation 1 convert to equivalent circuit
For calculating output impedance ๐๐ = 0, the above circuit simplified to
๐๐ = (^) ๐^1 ๐ ||๐
๐ธ โดLow resistance || high resistance โ
Low resistance โด (^) ๐^1 ๐ โช ๐
๐ธ
๐
Differential pair or Amplifier:
๏ The differential-pair or differential-amplifier is the most widely used building block in analog integrated-circuit design. For instance, the input stage of every op-amp is a differential amplifier.
๏ The BJT differential amplifier is the basis of a very-high-speed logic circuit family like emitter- coupled logic (ECL).
๏ Differential Amplifiers is an amplifier in which the output voltage is directly proportional to the difference of input signal. This amplifier, also called a diff-amp There are two input terminals and one output terminal ๐ฝ๐ = ๐จ๐ฝ๐ถ(๐ฝ๐ โ ๐ฝ๐) Where A vo is called the open-loop voltage gain.
The differential-mode input voltage ๐ฝ๐
= ๐ฝ๐ โ ๐ฝ๐
The common-mode input voltage ๐ฝ๐๐ = ๐ฝ๐+๐ฝ ๐ ๐
The BJT Differential Pair:
๏ The basic BJT differential pair is shown in fig.
Fig. The basic BJT differential pair
Fig: Differential pair with a small differential input signal
๏ From Fig, It can be seen that we are able to steer the entire bias current from one side of the pair to the other with small difference voltages. This current steering property of the differential pair allows it to be used in logic circuits. ๏ Apply a very small differential signal, which will result in one of the transistors conducting a
current of (^) ๐๐ฐ + ๐ซ๐ฐ ; the current in the other transistor will be ๐ฐ๐ โ ๐ซ๐ฐ..
๐ฝ๐ = ๐ฝ๐ช๐ โ ๐ฝ๐ช๐ = [๐ฝ๐ช๐ช โ (๐ฐ ๐ ๐ธโ โ๐ฐ) ๐น๐ช] โ [๐ฝ๐ช๐ช โ (๐ฐ ๐ ๐ธ+ โ๐ฐ) ๐น๐ช] = ๐โ๐ฐ๐น๐ช
A voltage difference is created between vC 2 and vC 1 when a differential-mode input voltage is applied.
The magnitude of the small-signal collector current in each transistor is then ( gmvd ) / 2. ๐๐ = ๐๐ถ2 โ ๐๐ถ ๐๐ = [๐๐ถ๐ถ โ ๐ผ๐ถ2๐
๐ถ] โ [๐๐ถ๐ถ โ ๐ผ๐ถ1๐
๐ถ] = (๐ผ๐ถ1 โ ๐ผ๐ถ2)๐
๐ถ ๐๐ = [(๐ผ 2 ๐ + ๐๐ 2 ๐ ๐) โ (๐ผ 2 ๐ โ ๐๐ 2 ๐ ๐)] ๐
๐ถ
Differential mode gain: The ratio of the output signal voltage to the differential-mode input signal is called the differential-mode gain, Ad , which is ๐๐ = ๐๐๐๐๐
๐ถ
๐ฝ๐
^ = ๐๐๐น๐
๐ผ๐ 2 ๐๐^ =^
๐ผ๐ 2 ๐๐ In many cases output is taken at one collect terminal which is called a one-sided output
๐๐ = ๐๐๐ 2 ๐๐
๐ถ
๐จ๐
= ๐๐ ๐๐น ๐ช โด For Unbalanced output /Single output
Small signal analysis of BJT differential pair
