MULTISTAGE AMPLIFIERS AND DIFFERENTIAL AMPLIFIER

Cascode amplifier, Differential amplifier – Common mode and Difference mode analysis -MOSFET input stages – tuned amplifiers – Gain and frequency response – Neutralization methods.

1. MULTISTAGE AMPLIFIERS AND DIFFERENTIAL AMPLIFIER Dr. C.Helen Sulochana Professor/ECE

2. Cascode amplifier, Differential amplifier – Common mode and Difference mode analysis -MOSFET input stages – tuned amplifiers – Gain and frequency response – Neutralization methods. Unit 2 MULTISTAGE AMPLIFIERS AND DIFFERENTIAL AMPLIFIER

3. MULTISTAGE AMPLIFIERS Need for multistage Amplifiers: The performance of single stage amplifier is often insufficient, hence several stages may be combined forming a multistage amplifier.• In multistage amplifier , more than one amplifying stage is used to achieve greater voltage and power gain. output of one stage is fed as the input of the next stage. This type of connection of amplifiers is called cascading . The overall gain of a multistage amplifier is the product of the gains of the individual stage : Gain (A) = A1 * A2 * A3 * A4 * ...... *A N Gain in decibels Gain (A) dB =20 log A1 + 20 log A2 + 20 log A3 + 20 log A4 + ...... + 20 log A N )

4. Requirements of multistage amplifier Impedance matching(high input impedance) Voltage Gain should be high Large bandwidth Types of Multistage amplifiers  RC coupled transformer coupled direct coupled. 

5. Cascode amplifier Cascode amplifier is a two-stage amplifier circuit, consists of a common-emitter ( CE) stage in series with a common-base ( CB ) stage. It is a direct coupled amplifier Bandwidth of CB amplifier is wider (used in high frequency applications) than CE configuration, but input impedance is low. Therefore, CB stage is preceded by CE stage which has moderately high input impedance (kΩs). Cascode amplifier is used to improve performance at high frequencies by mitigating the Miller effect and provide high input/output isolation.  Q 1 - common-emitter transistor , Q 2 - common-base transistor , forming a cascode combination collector current of Q 1 equals the emitter current of Q 2. transistors Q 1 and Q 2 in cascade act as a single CE transistor with negligible internal feedback (negligible hre ) and very small output conductance for an open circuited input. The reduction in the “internal feedback” reduces the probability of oscillation and results in improved stability of the circuit and provide higher isolation between its input and output small value of hr for the cascode transistor pair is useful in tuned-amplifier design . input resistance and voltage gain are equal to the corresponding values for a single CE stage . The output resistance is equal to the CB value (2 M, which is much higher than the CE value of 40 K)

6.   A I1 =     Z i1 ie   Z 01   Z i2   Z 02   =   Voltage Gain Voltage gain ( A V1 ) of Q 1 stage(CE amplifier) is = =   -------(1) -------(2)   Voltage gain ( A V2 ) of Q 2 stage(CB amplifier) is R C​ is the collector load resistor of Q2 Voltage gain ( A V ) of cascode amplifier     Assume h oe R L < 0.1.so we use approximate model for the analysis Input resistance of 2 nd stage( Q 2) forms the load Z for the 1 st stage Q 1 . Small signal Analysis of Cascode amplifier

7. This is the same gain as a common-emitter amplifier with collector load R C With much higher bandwidth (due to low Miller effect) Better high-frequency performance Output Impedance High (due to common-base Q2) Output impedance( Z ) of cascode amplifier is the output impedance( Z 02 ) of Q 2 (CB amplifier) Z Z 02   Input Impedance input impedance( Z i ) of cascode amplifier is the input impedance( Z i1 ) of Q 1 (CE amplifier) Z i1 ie  

8. useful in wideband amplifier design used in the design of high-frequency tuned amplifier stages https://www.circuitstoday.com/cascode-amplifier advantages over a single amplifier Higher input and output impedances, wideband amplifier-Higher bandwidth,-Miller Effect can be removed Higher input and output isolation.-reduce reverse transmission-because there is no direct coupling from output to input  applications

9. Differential Amplifier Differential Amplifier is used to amplify the difference between two input signals . commonly used as the basic building block in analog IC design. v 1 , v 2 are two input signals and v o Is the output. In ideal differential amplifier output signal V o  is proportional to the difference between the two input signals - Differential Gain But practically output depends not only on the difference mode signals, but also on the common mode signal difference mode signals (difference of two input signals) common mode signals - - - -(1) - - - -(2) - - - -(4) - - - -(3) Adding (1)& (2) Adding (1) from (2) https://ece.poriyaan.in/topic/basic-differential-amplifier-20239/ https://eee.poriyaan.in/topic/basics-of-differential-amplifier-11537/ v o v o - Common mode Gain (average of two input signals) For ideal differential amplifier is infinite, while is zero

10. Emitter coupled Differential Amplifier Consists of two identical transistors (Q 1 and Q 2 ), whose emitters are connected together and biased by –V EE The collector of Q 1 and Q 2 are connected through resistors R C to a positive supply voltage V CC . Emitter coupled Differential Amplifier Assume R C1 = R C2 V 1 and V 2 - are the input signals to the base of the transistors output is taken across their collector terminals (V o1 and V o2 ). Operation two operating modes. i. Common mode ii. Differential mode For common mode, the signals with same magnitude and phase are applied to both the inputs. V1 = V2 = V. The output signals( V o1 , V o1 )at the collectors of both the transistors are 180° out of phase with their base signals. As the base signals of Q1 and Q2 are equal and in phase with each other, their collector voltages will also be in phase and equal. The output voltage V o = V o2 - V o1 is zero. Practically, a small output voltage is produced due to some minor dissimilarity between the two transistors. Input signals of Q 1  and Q 2  will produce in phase voltages across R E which provide a negative feedback. Therefore, gain of both the amplifiers is reduced and small output voltage is produced. Thus, the common mode gain of the amplifier is low due to this negative feedback provided by R E . Common Mode Operation For common mode, the signals with same magnitude and phase are applied to both the inputs. V 1  = V 2 = V The output signals( V o1 , V o2 )at the collectors of both the transistors are 180° out of phase with their base signals. As the base signals of Q1 and Q2 are equal and in phase with each other, their collector voltages will also be in phase and equal. output voltage V o = V o2 - V o1 is zero. Practically, a small output voltage is produced due to some minor dissimilarity between the two transistors

11. Differential Mode Operation In differential mode of operation, the two input signals V1 and V2 are of equal magnitude but opposite phase. i.e., V1 = -V2. For these input signals to be same magnitude and opposite phase, a center tapped transformer is used. During positive half cycle of V1, the input to Q1 is positive sinusoidal signal and the input to Q2 is negative sinusoidal signal. This can be achieved due to centre tapped transformer. At the collector of Q1 and Q2, the signals are 180° out of phase with respect to their input signals. The output voltage is the difference between the output of the individual transistors. Differential Mode Operation For differential mode, the signals with equal magnitude and opposite phase are applied to both the inputs. V 1  = - V 2 The output signals( V o1 , V o1 )at the collectors of both the transistors are 180° out of phase with their base signals. As the base signals of Q1 and Q2 are equal and opposite phase with each other, their collector voltages will also be in opposite phase and equal. output voltage V o = V o2 – (- V o1 ) amplitude of the output will be twice the amplitude of the voltage obtained at either collector total output of any differential amplifier can be expressed as, V o  = A d  V d  + A c  V c   In common mode R E  will provide a negative feedback But in differential mode, R E  will not introduce negative feedback( equal and opposite voltages appear across R E  and these two voltages cancel each other)  Differential mode Gain -------(1) Assume h oe R L < 0.1.so we use approximate model for the analysis Small signal Analysis of differential amplifier Two input signals(V 1  = V 2  ) are equal in magnitude and having 180° phase difference in between them. V 1  = - V 2  = V S /2

12. emitter currents I e1 and I e2 are equal in magnitude and 180° out of phase. They cancel each and the current through the emitter is zero.  two transistors are matched, their a.c . equivalent circuits are identical. A.c . equivalent circuit Differential mode gain -------(2) -------(1) Substituting (2) in (1) Since V d  = V 1  – V 2  = V S  / 2 – (-V S /2) = V S output is across the two collectors of the transistors Q1 and Q2, which are perfectly matched. -------(A) approximate model - (R S is small-neglected) g m = h fe / h ie

13. Common mode Gain Two input signals(V 1  = V 2  ) are equal in magnitude and phase. V 1  = V 2  = V S approximate model both the emitter currents I e1 = I e2 = I e , flows through RE in the same direction. A.c . equivalent circuit two transistors are matched, their a.c . equivalent circuits are identical. Common mode gain V c  = (V 1  + V 2 ) / 2 = V S   -------(1) =   -------(2) Substituting (2) in (1) =   -------(B) (R E >> R S and h ie )

14. It is the measure of ability of a differential amplifier to reject a common mode signal • CMRR is defined as the ratio of the differential voltage gain Ad to common mode gain Ac and is expresses in dB. Common Mode Rejection Ratio (CMRR):- Figure of merit Input resistance output resistance CMRR >>1 The CMRR of a DA can be improved by making the common mode gain as small as possible ( high R E ). One popular method to increase the value of R E using a Constant current source circuit. The R E is replaced by a transistor Q3 to give same Q point to the transistor Q1 and Q2 Now DA is less sensitive to noise (CMRR >>1) R i  = 2 h ie   (from (A) and (B)) CMRR =   Method to improve CMRR (R S is smail )

15. The input signals are given to both the input terminals and so it is called as " dual input ". The output is taken between the collectors of the two transistors . Hence, it is called as " balanced output ". As the output is the difference between the output of two collectors , it is called differential output . Thus, the amplifier is called dual input balanced output differential amplifier . Types of differential amplifier due to its inherent design and the use of negative feedback Features Applications Instrumentation amplifier i. High differential gain ii. Low common mode gain iii. High CMRR iv. High input impedance and low output impedance v. Large Bandwidth

16. Note For FET differential amplifier, replace the circuit and equivalent circuit with the following diagrams circuit Differential mode Common mode In the equations, replace R E by R S and R C by R D

17. used to amplify small signals(low amplitude) at radio frequencies to minimize distortion . Small Signal Tuned Amplifier – operate in class A mode Large Signal Tuned Amplifiers- class AB, B or C amplifiers amplify the large signals( large amount of power) at radio frequencies. Tuned Amplifiers ( band pass amplifier or narrow band amplifer )   used in receiver to pick up and amplify the desired radio frequency signal and reject the other frequencies, An amplifier which amplifies a specific frequency is called tuned voltage amplifier or tuned amplifier. Application( Need  ) When the load amplifier circuit is replaced by a tuned( resonant circuit) circuit, then it is a Tuned amplifier circuit.

18. Class A Amplifier Q-point within the middle of its load line conduct current over the full 360 degrees of the input cycle Class B Amplifier Class AB Amplifier Class C Amplifier Q point is at an extreme end of its characteristic conduct current for only one-half a cycle (180 degree) Q point is between the two extremes for Class A and Class B . conduct current for more than half cycle, but less than one cycle . conduct current for less than half cycle , less than 180 degrees Used in radio frequency (RF) applications

19. SINGLE TUNED AMPLIFIERS Multistage amplifiers that use only one parallel tuned circuit as a load , each stage is tuned to the same frequency. two types . i . Capacitance coupled amplifiers ii . Inductance or transformer coupled amplifiers Output across the tuned circuit( resonant circuit) is coupled to the next s tage through the coupling capacitor . resonant circuit consists of an inductor (L) and a capacitor (C) connected in parallel R 1 , R 2  and R E  are called biasing resistors since these provide the operating current and voltage Capacitance Coupled Single Tuned Amplifiers- Class C Tuned Amplifier At resonance When input signal frequency increases , the inductive reactance (X L ) increases and the capacitive reactance ( X C ) decreases . At a certain frequency, the inductive reactance X L is equal to the capacitive reactance X C . This frequency is called resonance frequency ( f o ) The L and C values are selected such that the frequency to be amplified is equal to the resonant frequency A CE amplifier with tuned circuit as a load can be used as a single tuned amplifier conduction occurs for much less than 180 degrees circuit diagram

20. Response(gain) of tuned amplifier is maximum at resonance frequency . The tuned amplifier is designed to reject all frequencies below the lower cut off(half power) frequency f L  and above the upper cut-off frequency f H Gain drops to 1/ or 0.707 of its maximum value at f H and f L .   Resonance Curve- Frequency response At frequency The range of frequencies at which the voltage gain of the tuned amplifier falls to 70.7% of the maximum gain is called its Bandwidth. At resonance the impedance of the circuit becomes maximum and current is minimum. Impedance , R -coil resistance Current =

21. Q-Factor( quality factor ) For better selectively, the resonance curve should be very sharp, i.e., impedance should be decreased rapidly if the frequency is varied above and below the resonant frequency . Q factor is defined as the ratio of inductive reactance at resonance to the circuit resistance. It is the voltage magnification that the circuit produce at resonance Also defined as measure of efficiency with which inductor can store the energy . For series circuit Unloaded Q- when the tank circuit is not connected to the load Loaded Q- when the tank circuit is connected to external load Relation between Q and Bandwidth Relation between Q and Bandwidth sharpness of a resonance = Bandwidth/Resonant Frequency dissipation factor (D) that can be referred to as the total loss within a component is defined as 1/Q. dissipation factor (total loss within a component)

22. =   -------(1) Small signal Analysis of tuned amplifier Z L ​ ( f ) is the frequency-dependent impedance of the parallel RLC tank circuit. Substitute(2) into (1) -------(2) At Resonance, f = f , ​ Magnitude of Voltage Gain in (3) is represented as -------(3) (Maximum gain) and reactive parts cancel, Z L ​ = R (equation 2) maximum gain at f ​ , and reduced gain as f moves away from f ​ . R - effective load resistance(inductor's coil resistance + parallel load resistance) of the LC tank circuit R , L , C are in parallel . larger R ⇒ higher gain, narrower bandwidth -------(4)

23. 3 dB Gain is the ratio of maximum gain to Equating gain at -3dB point Solving (5) -------(5)

24. Amplifier with reduced bandwidth may not be able to amplify equally the complete band of signals and result in poor reproduction, this is called potential instability in tuned amplifier Efficiency highly frequency selective to select the desired carrier frequency Selectivity ↑ Q factor ↑ BW↓ Recovery of signal-poor Drawbacks of Single Tuned Amplifier

25. DOUBLE-TUNED VOLTAGE AMPLIFIER- synchronous tuning two tuned circuits are inductively coupled to each other and tuned to same frequency- synchronous tuning   L1 ,C1 is used as collector load L2 ,C2 is used as output circuit. R1 , R2, RE provide dc current and voltage for the transistor . circuit provides high impedance to the input signal and a large output appears across the tuned circuit L 1  C 1 . This output is inductively coupled to L 2  C 2  tuned circuit. Frequency response Advantages provides high selectivity, high gain and large bandwidth . used in radio and television receiver . When the coils are spaced apart, the flux linkages of primary coil L 1  will not link the secondary coil L 2 . The coils are said to have  Loose coupling . when the primary and secondary coils are brought close together, they have  Tight coupling .  Bandwidth BW= kf   K = coefficient of coupling, and f o  = resonant frequency. Disadvantages their alignment is difficult(synchronous tuning) circuit diagram Note   Except circuit diagram and frequency response , Other explanations are same as the single tuned amplifier

26. STAGGER-TUNED AMPLIFIER Two or more tuned circuits are cascaded The tuned circuits are tuned to slightly different frequencies. This amplifier has a greater bandwidth and flatter passband , if more number of stages are used. Large Q BW less than 6% of resonance frequency. therefore it is called as narrow band amplifier overall frequency response of a stagger tuned amplifier is obtained by adding individual response together . maximum flatness around the center frequency f .   bandwidth √2 times that of each individual single tuned circuits . overall selectivity is same as single stage double tuned amplifier. frequency response Advantages  increased bandwidth Disadvantages   reduced selectivity critical tuning of many tank circuits circuit diagram Note   Except circuit diagram and frequency response , Other explanations are same as single tuned amplifier

27. Advantages of Tuned Amplifiers They amplify the desired frequencies Good SNR Suitable for radio transmitters and receivers The range of frequencies can be varied. Disadvantages of Tuned Amplifiers Not suitable for amplifying audio frequencies If band of frequency is increased, design becomes complex Circuit is bulky and expensive used in radio receivers to amplify a particular band of frequencies used as an output RF amplifiers in radio transmitters to increase the output efficiency and to reduce the harmonics. used in active filters such as low pass, high pass and band pass to allow amplification of signal only in the desired narrow band. Applications of Tuned Amplifiers

28. Comparison of Tuned Amplifiers

29. Neutralization Neutralization in tuned amplifier is a technique to prevent oscillation and stabilize the circuit by canceling unwanted feedback(base –collector) at high-frequencies. The stage gain should be reduced to prevent oscillations in the circuit. This can be done by Reducing Q Stagger tuning Loose coupling between the stages Neutralization Methods(types) A portion of output signal is feedback to the input with same amplitude but opposite phase to cancel the unwanted feedback signal Hazeltine Neutralization Neutrodyne Neutralization Rice Neutralization Neutralization using coil Oscillations degrade the performance of the tuned amplifier In tuned amplifiers, a t resonance frequency, the junction capacitance between base and collector of the transistor becomes dominant. Thus the reactance of the circuit is low . This reactance provides a positive feedback which causes oscillations in the circuit and makes the system unstable . To prevent oscillation in tuned amplifiers, the neutralization technique is used. Need for Neutralization Gain reduction method( How is neutralization achieved in amplifiers )

30. a small amount of variable capacitance CN is connected from the bottom of the coil(inductor) to the base of the transistor. The output coil is center-tapped and the tap is used as the power supply feedpoint of the amplifier. This capacitance feeds a signal with equal amplitude and opposite phase , which cancels the signal feed by the internal capacitance Cbc from the top end of the coil . Dis adv. -capacitance value changes with time and supply voltage Hazeltine neutralization . Neutrodyne neutralization technique, the neutralization capacitor is connected from the lower end of base coil of the next stage to the base of the transistor. The circuit functions as the Hazeltine neutralization circuit Neutrodyne neutralization Advantage - capacitor is not connected with V CC  and it is not sensitive to changes in the supply voltage. It also provides high stability.

31. Neutralization using coil part of the tuned circuit at the base of next stage is used for minimum coupling to other windings . The voltage across the inductor will cancel the feedback signal produced by the collector base capacitance Cbc It uses a center tapped coil in the base circuit . The signal voltages at the end of the tuned base coil are equal and out of phase. Rice Neutralization

32. Problem 1

33. Problem 2

34. Problem 3

35. Problem 4