# BJT Amplifier. Superposition principle (linear amplifier)

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1 BJT Amplifier Two types analysis DC analysis Applied DC voltage source AC analysis Time varying signal source Superposition principle (linear amplifier) The response of a linear amplifier circuit excited by multiple independent input signals is the sum of the responses of the circuit to each of the input signals alone.

2 Bipolar linear amplifier Variable i B, v BE I B, V BE i b,v be I b, V be Meaning Total instantaneous values DC values Instantaneous ac values Phasor values

3 Common Emitter with Time-Varying Input

4 I B versus V BE Characteristic I be i B BQ (1 + ) = B + VT v I i b

5 Total Harmonic Distortion (THD) ( ) THD % = V 2 n V 1 2

6 ac Equivalent Circuit for Common Emitter

7 Small-Signal Hybrid π Model for npn BJT g r π g m m = r = π I V CQ T βv I T CQ = β Phasor signals are shown in parentheses.

8 Small-Signal Equivalent Circuit Using Common-Emitter Current Gain

9 Small-Signal Equivalent Circuit for npn Common Emitter circuit-voltage gain A v = ( g m C )( r π r π + B )

10 Calculate the small-signal voltage gain of the BJT as shown in figure. Assume the transistor and circuit parameters are β = 100, V CC =12 V, V BE = 0.7 V, C = 6 k Ω, B = 50 kω, and V BB =1.2 V.

11 Problem-Solving Technique: BJT AC Analysis 1. Analyze circuit with only dc sources to find Q point. 2. eplace each element in circuit with smallsignal model, including the hybrid π model for the transistor. 3. Analyze the small-signal equivalent circuit after setting dc source components to zero.

12 Hybrid π Model for npn with Early Effect CQ A o I V r = + = A CE V v s c V v e I i T BE 1. 1 pt Q CE c o v i r = ) )( ( B o C m v r r r g A + = π π

13 Hybrid π Model for pnp with Early Effect A v = ( g m r π r )( r o π + C B )

14 BJT Amplifier configurations Common emitter Basic common emitter amplifier With Emitter resistor With bypass capacitor Common collector (emitter follower) Common base

15 4 Equivalent 2-port Networks Voltage Amplifier Current Amplifier

16 4 Equivalent 2-port Networks Transconductance Amplifier Transresistance Amplifier

17 Common Emitter with Voltage-Divider Bias and a Coupling Capacitor

18 Small-Signal Equivalent Circuit Coupling Capacitor Assumed a Short

19 npn Common Emitter with Emitter esistor

20 Small-Signal Equivalent Circuit: Common Emitter with E ) ( ) (1 ) (1 2 1 S i i E C v ib i E ib r A r = = + + = β β β π π

21 E and Emitter Bypass Capacitor

22 Frequency epsonse Chapter 7 (Neamen Book) Sections

23 Operational Amplifier (Op Amp) Amplifies the difference between two input signals to give an output signal transistors Ideal op-amp equivalent circuit

24

25 Equivalent circuit: Op-amp 741

26 Op-Amp Ideal Inverting T-network Effect of finite gain Summing amplifier Non-inverting voltage follower Applications current to voltage converter voltage-to-current converter difference amplifier integrator & differentiator precision half-wave rectifier

27 Small-Signal Equivalent Circuit: MOSFET with Input and Output Feedback v v O I = F I

28 Equivalent Circuit of Op-Amp Output voltage is limited: biased by dc voltages V + and V - v o V +, it will saturate or limited to a value nearly equal to V +, similar for V -. V - + V <v o <V + - V

29 Inverting Op-Amp Equivalent circuit

30 Inverting Op-Amp with T-Network 2 3 A v = ( )

31 Inverting Op-Amp with Finite Differential-Mode Gain A v = 2 1 [1 + 1 A od 1 ( )]

32 Field Effect Transistors (FET) Metal-Oxide Semiconductor FET (MOSFET) n-type MOS p-type MOS Junction FET (JFET) pn junction FET

33 MOSFET Smaller in size High VLSI density Based on field enhancement Modulation of conductance of semiconductor substrate Basic MOS capacitor structure

34 Understanding the field enhancement p-type

35 p-type substrate: +ve gate voltage n-type substrate: -ve gate voltage n-type

36 n-channel enhancement mode MOSFET Channel length, L ~ 1 µm Oxide length, t ox ~ 400 Angstrom NMOS (carriers are electrons) p-type substrate, two n-regions (n-source, n-drain) Positive Gate voltage

37 Basic transistor operation Induced n-type channel Depletion region Cross-section of n-channel MOSFET prior to formation of electron inversion layer Cross-section after the formation of electron inversion layer

38 Threshold voltage V TN : applied gate voltage required to create an inversion charge in which the density is equal to the concentration of majority carriers in semiconductor substrate. voltage at which the device turns ON V GS < V TN, No current V GS < V TN, current flow (drain to source) Gate and drain voltages are measured with respect to source

39 Thickness of inversion layer gives the relative charge density V DS increases, the voltage drop across the oxide near the drain terminal decreases Decrease in induced charge density Decrease in incremental conductance

40 V GS -V DS (sat)=v TN V DS (sat)=v GS -V TN V DS increases to a point where the potential difference between gate and drain terminals (V GS -V DS ) becomes equal to the threshold voltage Induced charge density at drain terminal becomes zero Incremental conductance subsequently zero

41 Family of curves Ideal current-voltage characteristics

42 PMOS n-type substrate, two p-regions (p-source, p-drain) Gate voltage???, carriers??

43 Circuit symbols NMOS PMOS

44 NMOS Common-Source Circuit Variable i D,v GS I D,V GS i d,v gs I d,v gs Symbol meaning Total instantaneous values DC values Instantaneous ac values Phasor values

45 NMOS Transistor Small-Signal Parameters Values depends on Q-point ] [ ] ) ( [ ) ( 2 ) ( 2 = = = = = = DQ TN GSQ n o v i o DQ n TN GSQ n m gs d v i m I V V K r r I K V V K g v i g DS D GS D λ λ Transconductance (relates output current to input voltage) -can think as gain of a transistor

46 Simple NMOS Small-Signal Equivalent Circuit

47 NMOS Common-Source Circuit AC Small-signal A v = V o V i = g m ( r ) D o

48 Problem-Solving Technique: MOSFET AC Analysis 1. Analyze circuit with only the dc sources to find quiescent solution. Transistor must be biased in saturation region for linear amplifier. 2. eplace elements with small-signal model. 3. Analyze small-signal equivalent circuit, setting dc sources to zero, to produce the circuit to the time-varying input signals only.

49 MOSFET Amplifier Configurations Common source Common drain (source follower) Common gate Input and output resistance characteristics are important in determining loading effects

50 Common-Source Configuration DC analysis: Coupling capacitor is assumed to be open. AC analysis: Coupling capacitor is assumed to be a short. DC voltage supply is set to zero volts.

51 Small-Signal Equivalent Circuit A v = V o V i = g m ( r o D )( i i + Si ) Output resistance can be calculated by setting the independent input source V i =0 i.e. V gs =0. = o D r o

52 DC Load Line Q-point near the middle of the saturation region for maximum symmetrical output voltage swing,. Small AC input signal for output response to be linear.

53 Example Determine the small-signal voltage gain and input and output resistances of a common source amplifier. For the circuit, the parameters are: V DD =10 V, 1 =70.9 kω, 2 =29.1 kω, and D =5 kω. The transistor parameters are V TN = 1.5 V, K n =0.5 ma/v 2, and λ =0.01 V -1. Assume si = 4 kω.

54 Common-Source Amplifier with Source esistor Source resistor is used to stabilize the Q-point against transistor parameter variation - decreases the gain Determine the small-signal voltage gain of a common-source circuit containing a source resistor. The transistor parameters are V TN = 0.8 V, K n = 1 ma/v 2, and λ =0. A v = -5.76

55 Small-Signal Equivalent Circuit for Common-Source with Source esistor V = g o m V gs Use of KVL from input around the gate-source loop V = V + i gs g m V gs D s A v g = 1 + g m m D If g m is very large, S A v V S gs D V = 1+ g i m s

56 Common-Source Amplifier with Bypass Capacitor Small-signal equivalent circuit To minimize the loss in small-signal voltage gain as in previous example, while maintaining the Q-point stability, a bypass capacitor can be added, or replacing the source resistor by a constant current source.

57 Determine the small-signal voltage gain of a common-source circuit biased with a constant current source and incorporating a source bypass capacitor. The transistor parameters are V TN = 0.8 V, K n = 1 ma/v 2, and λ =0.

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