ECE 271 Electronic Circuits I

ECE 271 Electronic Circuits I Topic 6 Analog Circuits Ideal Operational Amplifiers One Transistor Amplifier Topic 6 - 1 NJIT ECE Dr. Serhiy Levkov

Example of Analog Electronic System: FM Stereo Receiver
Much information in the world (temperature, pressure, light intensity, sound, etc.) is analog in nature. In electric form those signals are transformed by different linear and nonlinear functions. Linear functions: Radio and audio frequency amplification, frequency selection (tuning), impedance matching, local oscillator Nonlinear functions: DC power supply(rectification), frequency conversion (mixing), detection/demodulation The characteristics of signals are most often manipulated with linear amplifiers. Topic 6 - 2 NJIT ECE Dr. Serhiy Levkov

Amplification: Introduction
Example: Audio amplifier. The input is a form of complicated periodic signal. A complex periodic signal can be represented as the sum of many individual sine waves, one component of which has amplitude Vi = 1 mV and frequency ws with 0 phase (signal is used as reference): After amplification, linear amplifier output is sinusoidal with same frequency but different amplitude VO and phase : Topic 6 - 3 NJIT ECE Dr. Serhiy Levkov

Amplification: Introduction (cont.)
Amplifier output power is: If we need to deliver PO = 100 W and have RL = 8 W, then This power results in output current: where Input current is given by (Vi = 1 mV ) and the phase is zero because circuit is purely resistive. Topic 6 - 4 NJIT ECE Dr. Serhiy Levkov

Amplification: Gain The main parameter of an amplifier is the gain. Using phasor representation , we can introduce three types of gain. Voltage Gain (complex number): Magnitude and phase of voltage gain are given by and For our example, Current Gain: Magnitude of current gain is given by Topic 6 - 5 NJIT ECE Dr. Serhiy Levkov

Amplification: Gain (cont.)
Power Gain: For our example, The gain is often expressed in decibel scale: Topic 6 - 6 NJIT ECE Dr. Serhiy Levkov

Two-port Model for Amplifier
Type of input-output model, black box that relates outputs to inputs. input output x1 x2 Amplifier Simplifies amplifier-behavior modeling in complex systems. Two-port (four terminal) models are linear network models, valid only under small-signal conditions. Represented by g-, h-, y- and z-parameters. (v1, i1) and (v2, i2) represent signal components of voltages and currents at the network ports. Topic 6 - 7 NJIT ECE Dr. Serhiy Levkov

Two-port Model Parameters
Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Topic 6 - 8 NJIT ECE Dr. Serhiy Levkov

Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Impedance (z)-parameters Admittance (y)-parameters Topic 6 - 9 NJIT ECE Dr. Serhiy Levkov

Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Impedance (z)-parameters Admittance (y)-parameters Hybrid (h)-parameters Inverse hybrid (g)-parameters Topic NJIT ECE Dr. Serhiy Levkov

Theoretically, two-port model could be described fully by a 4x4 matrix or 16 parameters. In practice, several sets of 4 parameters are used. Impedance (z)-parameters Admittance (y)-parameters Hybrid (h)-parameters Inverse hybrid (g)-parameters Transfer (A,B,C,D) -parameters Topic NJIT ECE Dr. Serhiy Levkov

g-parameters Use open-circuit (i = 0) and short-circuit (v = 0) terminal conditions Open-circuit input conductance Reverse short-circuit current gain Forward open-circuit voltage gain Short-circuit output resistance Topic NJIT ECE Dr. Serhiy Levkov

g-parameters Use open-circuit (i = 0) and short-circuit (v = 0) terminal conditions Open-circuit input conductance Reverse short-circuit current gain Forward open-circuit voltage gain Short-circuit output resistance Norton transformation If g12 = 0 Topic NJIT ECE Dr. Serhiy Levkov

g-parameters: Example
Problem: Find g-parameters. Approach: Apply specified boundary conditions for each g-parameter, use circuit analysis. For g11 and g21: apply voltage v1 to input port and open circuit output port. For g12 and g22: apply current i2 to output port and short circuit input port. For g11: -v1 + i1*20k + (i1 + 50*i1)*200k = 0  i1=v1/(20k + 51*200k) For g21: v2 = 51*i1*200k = 51*200k*v1/(20k + 51*200k) = 51*200k*g11*v1 Topic NJIT ECE Dr. Serhiy Levkov

Ideal Voltage Amplifier
Consider amplifier with g12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. Topic NJIT ECE Dr. Serhiy Levkov

Consider amplifier with g12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. Conclusion: full gain depends on source and load parameters. Topic NJIT ECE Dr. Serhiy Levkov

Consider amplifier with g12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. How to make it non- dependent? Conclusion: full gain depends on source and load parameters. Topic NJIT ECE Dr. Serhiy Levkov

Consider amplifier with g12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. How to make it non- dependent? Rin >> Rs and Rout<< RL, Ideal voltage amplifier: Rout = 0, Conclusion: full gain depends on source and load parameters. Topic NJIT ECE Dr. Serhiy Levkov

Consider amplifier with g12 = 0 (typical voltage amplifier) that includes source and load resistances and calculate the voltage gain from the source voltage to load voltage. How to make it non- dependent? Rin >> Rs and Rout<< RL, Ideal voltage amplifier: Rout = 0, For current: Conclusion: full gain depends on source and load parameters. Topic NJIT ECE Dr. Serhiy Levkov

Other Amplifier Types Voltage amplifier Current amplifier
Transconductance amplifier Transresistance amplifier Topic NJIT ECE Dr. Serhiy Levkov

Operational Amplifier (Op Amp)
Op amp is a fundamental building block in electronic design. They are cheap mass produced IC and can be used to build many different types of electronic devices like instrumentation amplifiers, active filters, rectifiers, A/D and D/A converters, and others. Typical integrated circuit amplifier: LM386N (~ $1.00 each) The practical op amp is a form of differential amplifier: responds to a difference of two input signals. Typically: VCC >0, VEE <0 – so the voltages are symmetric 5V, 10V, 18V. Topic NJIT ECE Dr. Serhiy Levkov

Differential Amplifier – Signal Amplification
The typical voltage transfer characteristic for a differential amplifier biased by two symmetric power supplies: A - open-circuit voltage gain, A =10, Adb =20log(10) = 20 db vID = (v+-v--) - differential input signal vID = VID + vid = sin t, where VID – dc value, vid – signal component vO = VO + vo = sin t Topic NJIT ECE Dr. Serhiy Levkov

Distortion in Amplifiers
If the ac input signal exceeds 0.5V, the output signal will be clipped off (see vO2 ) and get distorted. Different gains for positive and negative values of input also cause distortion in output. Total Harmonic Distortion (THD) is a measure of signal distortion that compares undesired harmonic content of a signal to the desired component. desired output 2nd harmonic distortion dc 3rd harmonic distortion Topic NJIT ECE Dr. Serhiy Levkov

Differential Amplifier Model: Basic
The basic model of differential amplifier is represented by: A - open-circuit voltage gain vid = (v+-v-) = differential input signal voltage Rid - amplifier input resistance Ro - amplifier output resistance Signal developed at amplifier output is in phase with the voltage applied at + input (non-inverting) terminal and 180o out of phase with that applied at - input (inverting) terminal. Topic NJIT ECE Dr. Serhiy Levkov

Differential Amplifier Model: With Source and Load
RL = load resistance RS = Thevenin equivalent resistance of signal source vs = Thevenin equivalent voltage of signal source Topic NJIT ECE Dr. Serhiy Levkov

Differential Amplifier Model: With Source and Load
RL = load resistance RS = Thevenin equivalent resistance of signal source vs = Thevenin equivalent voltage of signal source and Topic NJIT ECE Dr. Serhiy Levkov

Differential Amplifier Model: With Source and Load (Example)
Problem: Calculate voltage gain Given Data: A=100, Rid =100kW, Ro = 100W, RS =10kW, RL =1000W Topic NJIT ECE Dr. Serhiy Levkov

Differential Amplifier Model: With Source and Load (Example)
Problem: Calculate voltage gain Given Data: A=100, Rid =100kW, Ro = 100W, RS =10kW, RL =1000W Ideal amplifier’s output depends only on input voltage difference and not on source and load resistances. This can be achieved by using resistance condition (Rid >> RS or infinite Rid and Ro << RL or zero Ro ): A - open-loop gain (maximum voltage gain available from the device) Topic NJIT ECE Dr. Serhiy Levkov

Ideal Operational Amplifier
Ideal op amp is a special case of ideal differential amplifier with: - infinite gain, - infinite Rid , - zero Ro . Topic NJIT ECE Dr. Serhiy Levkov

Ideal op amp is a special case of ideal differential amplifier with: - infinite gain, - infinite Rid , - zero Ro . Thus: 1. Input voltage is zero, vid =0 for any finite output voltage (since A is infinite). 2. Input currents are zero, i+ =0 and i-=0 (since Rid is infinite). Topic NJIT ECE Dr. Serhiy Levkov

Ideal op amp is a special case of ideal differential amplifier with: - infinite gain, - infinite Rid , - zero Ro . Thus: 1. Input voltage is zero, vid =0 for any finite output voltage (since A is infinite). 2. Input currents are zero, i+ =0 and i-=0 (since Rid is infinite). Additional properties: infinite common-mode rejection (rejects input signals common to both inputs) infinite open-loop bandwidth (frequency magnitude response is flat everywhere with zero phase shift) infinite output voltage range ( in practice limited by VS+ and VS- ) infinite output current capability infinite slew rate (rate of change of output voltage) zero input-offset voltage (when the input terminals are shorted, vout = 0) The major benefit of ideal op-amp: the same standard op-amp allows to build various circuits with very specific properties by using external to op-amp circuit elements. The classic op-amps circuits are considered further. Topic NJIT ECE Dr. Serhiy Levkov

Inverting Amplifier: Configuration
Non-inverting input is grounded. Feedback network (resistor R2 ) is connected between inverting input and output Input network (resistor R1 ) is connected between inverting input and signal source. Topic NJIT ECE Dr. Serhiy Levkov

Inverting Amplifier:Voltage Gain
Topic NJIT ECE Dr. Serhiy Levkov

Substituting iS and i2 into KVL: Topic NJIT ECE Dr. Serhiy Levkov

Substituting iS and i2 into KVL: Conclusions: The gain of the inverting op-amp circuit is determined by R1 and R2 . The gain is a result of imposing the negative feedback. Gain is greater than 1 if R2 > R1. Gain is less than 1 if R1 > R2 Negative voltage gain implies 1800 phase shift between input and output signals. Inverting input of op amp is at ground potential (not connected directly to ground) and is said to be at virtual ground. Topic NJIT ECE Dr. Serhiy Levkov

Inverting Amplifier: Input and Output Resistances

Inverting Amplifier: Input and Output Resistances
But i1=i2 (i- =0) Since v- = 0, i1=0 and vx = 0 irrespective of the value of ix , Rout is found by applying a test current (or voltage) source to amplifier output, turning off all independent sources and determining the voltage (or current): Topic NJIT ECE Dr. Serhiy Levkov

Inverting Amplifier: Example
Problem: Design an inverting amplifier with Av=40 dB, Rin =20kW, Assumptions: Ideal op amp Convert the gain from db: Input resistance is controlled by R1 and voltage gain is set by R2 / R1. Thus and Topic NJIT ECE Dr. Serhiy Levkov

Summing Amplifier Since i-=0, i3= i1 + i2,
vid Scale factors for the 2 inputs can be independently adjusted by proper choice of R2 and R1. Any number of inputs can be connected to summing junction through extra resistors. This is an example of a simple digital-to-analog converter. Since negative amplifier input is at virtual ground (vid = 0): Topic NJIT ECE Dr. Serhiy Levkov

Non-inverting Amplifier: Configuration
Input signal is applied to the non-inverting input terminal. Portion of the output signal is fed back to the negative input terminal. Analysis is done by relating voltage at v1 to input voltage vs and output voltage vo . Topic NJIT ECE Dr. Serhiy Levkov

Non-inverting Amplifier: Analysis
+ - vid i- i+ Since i-=0, (voltage divider) Topic NJIT ECE Dr. Serhiy Levkov

+ - vid i- i+ Since i-=0, From KVL Topic NJIT ECE Dr. Serhiy Levkov

+ - vid i- i+ Since i-=0, From KVL , since vid =0  and  Topic NJIT ECE Dr. Serhiy Levkov

+ - vid i- i+ Since i-=0, From KVL , since vid =0  and  . Topic NJIT ECE Dr. Serhiy Levkov

+ - vid i- i+ Since i-=0, From KVL , since vid =0  and  . Since i+=0, Topic NJIT ECE Dr. Serhiy Levkov

+ - vid i- i+ Since i-=0, From KVL , since vid =0  and  . Since i+=0, Rout is found by applying a test current source to amplifier output and setting vs = 0 and is identical to the output resistance of inverting amplifier i.e. Rout =0. Topic NJIT ECE Dr. Serhiy Levkov

Non-inverting Amplifier: Example
+ - vid i- i+ Problem: Determine the characteristics of given non-inverting amplifier. Given Data: R1= 3kW, R2 =43kW, vs=+0.1 V Assumptions: Ideal op amp. Analysis: Since i-=0, io Topic NJIT ECE Dr. Serhiy Levkov

Voltage Follower (Unity-gain Buffer)

Voltage Follower (Unity-gain Buffer)
A special case of non-inverting amplifier, also called voltage follower with infinite R1 and zero R2. Hence Provides excellent impedance-level transformation while maintaining signal voltage level. Ideal voltage buffer does not require any input current and can drive any desired load resistance without loss of signal voltage. Unity-gain buffer is used in many sensor and data acquisition systems. Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier A combination of inverting and non-inverting amplifier. Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier A combination of inverting and non-inverting amplifier. Also, (voltage division) Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier A combination of inverting and non-inverting amplifier. Since v-= v+, For R2= R1, Also, (voltage division) Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier A combination of inverting and non-inverting amplifier. Since v-= v+, For R2= R1, The circuit amplifies difference between input signals (differential subtractor). Also, (voltage division) Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier A combination of inverting and non-inverting amplifier. Since v-= v+, For R2= R1, The circuit amplifies difference between input signals (differential subtractor). To understand better, use superposition: For v2=0, Rin1= R1, the circuit reduces to an inverting amplifier with the gain – R2 /R1 : vO1= (– R2 /R1 ) v1 For v1=0, v2 is attenuated by the voltage divider and then amplified by non-inverting gain 1+R2 /R1: vO2= (R2 /(R1 +R1 ))(1+ R2 /R1 ) v2 Then vO = vO1 + vO2,  Also, (voltage division) Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier: Example
Do example on the board Topic NJIT ECE Dr. Serhiy Levkov

Difference Amplifier: Example
Problem: Determine Vo, V+, V-, Io, I1, I2, I3 . Given Data: R1= 10kW, R2 =100kW, V1= 5V, V2=3V Assumptions: Ideal op amp. Hence, V-= V+ and I-= I+= 0. Analysis: Topic NJIT ECE Dr. Serhiy Levkov

Integrator Topic NJIT ECE Dr. Serhiy Levkov

Integrator Feedback resistor R2 in the inverting amplifier is replaced by capacitor C. The circuit uses frequency-dependent feedback. Topic NJIT ECE Dr. Serhiy Levkov

Integrator Since ic= is ,
Feedback resistor R2 in the inverting amplifier is replaced by capacitor C. The circuit uses frequency-dependent feedback. Topic NJIT ECE Dr. Serhiy Levkov

Voltage at the circuit’s output at time t is given by the initial capacitor voltage plus integral of the input signal from start of integration interval, here, t=0. Feedback resistor R2 in the inverting amplifier is replaced by capacitor C. The circuit uses frequency-dependent feedback. Topic NJIT ECE Dr. Serhiy Levkov

Voltage at the circuit’s output at time t is given by the initial capacitor voltage plus integral of the input signal from start of integration interval, here, t=0. Voltage at the circuit’s output at time t is given by the initial capacitor voltage plus integral of the input signal from start of integration interval, here, t=0. Integration of an input step signal results in a ramp at the output. Feedback resistor R2 in the inverting amplifier is replaced by capacitor C. The circuit uses frequency-dependent feedback. Topic NJIT ECE Dr. Serhiy Levkov

Differentiator Topic NJIT ECE Dr. Serhiy Levkov

Differentiator Input resistor R1 in the inverting amplifier is replaced by capacitor C. Topic NJIT ECE Dr. Serhiy Levkov

Differentiator Since iR= is
Input resistor R1 in the inverting amplifier is replaced by capacitor C. Topic NJIT ECE Dr. Serhiy Levkov

Input resistor R1 in the inverting amplifier is replaced by capacitor C. Output is scaled version of derivative of input voltage. Topic NJIT ECE Dr. Serhiy Levkov

Input resistor R1 in the inverting amplifier is replaced by capacitor C. Output is scaled version of derivative of input voltage. Derivative operation emphasizes high-frequency components of input signal, hence is less often used than the integrator. Topic NJIT ECE Dr. Serhiy Levkov

Op-Amps – What’s Next Frequency dependent feedback (cont. ch 10):
high, low and band pass amplifiers (filters) integrators and differentiators Topic NJIT ECE Dr. Serhiy Levkov

high, low and band pass amplifiers (filters) integrators and differentiators Analysis of non-ideal amplifiers (ch. 11) Amplifier frequency response and stability (ch. 11) Topic NJIT ECE Dr. Serhiy Levkov

high, low and band pass amplifiers (filters) integrators and differentiators Analysis of non-ideal amplifiers (ch. 11) Amplifier frequency response and stability (ch. 11) Op-amps applications (ch. 12) instrumentation amplifiers active filters D/A and A/D converters Oscillators Nonlinear circuits (precision rectifiers) Circuits with positive feedback (comparators, triggers) Topic NJIT ECE Dr. Serhiy Levkov

high, low and band pass amplifiers (filters) integrators and differentiators Analysis of non-ideal amplifiers (ch. 11) Amplifier frequency response and stability (ch. 11) Op-amps applications (ch. 12) instrumentation amplifiers active filters D/A and A/D converters Oscillators Nonlinear circuits (precision rectifiers) Circuits with positive feedback (comparators, triggers) Single transistor amplifiers – linear amplification and small signal model (ch. 13) Topic NJIT ECE Dr. Serhiy Levkov

high, low and band pass amplifiers (filters) integrators and differentiators Analysis of non-ideal amplifiers (ch. 11) Amplifier frequency response and stability (ch. 11) Op-amps applications (ch. 12) instrumentation amplifiers active filters D/A and A/D converters Oscillators Nonlinear circuits (precision rectifiers) Circuits with positive feedback (comparators, triggers) Single transistor amplifiers – linear amplification and small signal model (ch. 13) Single transistor amplifiers – detailed design (ch. 14) Topic NJIT ECE Dr. Serhiy Levkov

What do we study in this course?
Op-Amps – What’s Next Frequency dependent feedback (cont. ch 10): high, low and band pass amplifiers (filters) integrators and differentiators Analysis of non-ideal amplifiers (ch. 11) Amplifier frequency response and stability (ch. 11) Op-amps applications (ch. 12) instrumentation amplifiers active filters D/A and A/D converters Oscillators Nonlinear circuits (precision rectifiers) Circuits with positive feedback (comparators, triggers) Single transistor amplifiers – linear amplification and small signal model (ch. 13) Single transistor amplifiers – detailed design (ch. 14) Op-amps design (multistage amplifiers) (ch. 15) What do we study in this course? Topic NJIT ECE Dr. Serhiy Levkov

high, low and band pass amplifiers (filters) integrators and differentiators Analysis of non-ideal amplifiers (ch. 11) Amplifier frequency response and stability (ch. 11) Op-amps applications (ch. 12) instrumentation amplifiers active filters D/A and A/D converters Oscillators Nonlinear circuits (precision rectifiers) Circuits with positive feedback (comparators, triggers) Single transistor amplifiers – linear amplification and small signal model (ch. 13) Single transistor amplifiers – detailed design (ch. 14) Op-amps design (multistage amplifiers) (ch. 15) Topic NJIT ECE Dr. Serhiy Levkov

Transistors as Amplifiers
Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier What do we know: MOSFET (FET) can be used as amplifier if operated in saturation region (SR) Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier What do we know: MOSFET (FET) can be used as amplifier if operated in saturation region (SR) BJT can be used as an amplifier when biased in the forward-active region (FAR) Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier What do we know: MOSFET (FET) can be used as amplifier if operated in saturation region (SR) BJT can be used as an amplifier when biased in the forward-active region (FAR) We will refer to the FAR and SR as to the “active region” Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier What do we know: MOSFET (FET) can be used as amplifier if operated in saturation region (SR) BJT can be used as an amplifier when biased in the forward-active region (FAR) We will refer to the FAR and SR as to the “active region” In these regions, transistors can provide high voltage, current and power gains Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier What do we know: MOSFET (FET) can be used as amplifier if operated in saturation region (SR) BJT can be used as an amplifier when biased in the forward-active region (FAR) We will refer to the FAR and SR as to the “active region” In these regions, transistors can provide high voltage, current and power gains Bias is provided to stabilize the operating point in a desired operation region Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

In this section we will study The general techniques for employing individual transistors as amplifiers Operation of common source MOSFET amplifier Operation of common emitter BJT amplifier What do we know: MOSFET (FET) can be used as amplifier if operated in saturation region (SR) BJT can be used as an amplifier when biased in the forward-active region (FAR) We will refer to the FAR and SR as to the “active region” In these regions, transistors can provide high voltage, current and power gains Bias is provided to stabilize the operating point in a desired operation region The Q-point also determines Small-signal parameters of transistor Voltage gain, input resistance, output resistance Maximum input and output signal amplitudes Power consumption Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Consider a BJT , biased in active region by dc voltage source VBE = 0.7V. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Consider a BJT , biased in active region by dc voltage source VBE = 0.7V. From the simplified FAR model we get: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Consider a BJT , biased in active region by dc voltage source VBE = 0.7V. From the simplified FAR model we get: Thus the Q-point is set at (IC, VCE) = (1.5 mA, 5 V) Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Now let’s inject the sin signal with the amplitude 8 mV by adding the voltage source vbe The total base-emitter voltage becomes: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Now let’s inject the sin signal with the amplitude 8 mV by adding the voltage source vbe The total base-emitter voltage becomes: From the FAR model for VBEh = 0.708V and VBEl = 0.692V we will get Calculate actual IBh and Ibl on the board Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Now let’s inject the sin signal with the amplitude 8 mV by adding the voltage source vbe The total base-emitter voltage becomes: From the FAR model for VBEh = 0.708V and VBEl = 0.692V we will get Thus 8 mV peak change in vBE :  5 mA change in iB  and 0.5 mA change in iC. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier Now let’s inject the sin signal with the amplitude 8 mV by adding the voltage source vbe The total base-emitter voltage becomes: From the FAR model for VBEh = 0.708V and VBEl = 0.692V we will get Thus 8 mV peak change in vBE :  5 mA change in iB  and 0.5 mA change in iC. From the load line equation this will produce the 1.65V change in vCE . Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

BJT Amplifier If changes in operating currents and voltages are small enough, then iC and vCE waveforms are undistorted replicas of input signal. Small voltage change at base causes large voltage change at collector. Voltage gain is given by: Minus sign indicates 1800 phase shift between input and output signals. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

MOSFET Amplifier Doing similar analisis as for BJT, we get :
Consider MOSFET biased in active region by dc voltage source VGS = 3.5 V, which Will set the Q-point at (ID, VDS) = (1.56 mA, 4.8 V). Then we introduce the signal vGS and total gate-source voltage becomes Doing similar analisis as for BJT, we get : 1 V change in vGS  1.25 mA change in iD  4 V change in vDS. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Coupling and Bypass Capacitors
The constant voltage biasing is not a good method, 4 resistor is better. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The constant voltage biasing is not a good method, 4 resistor is better. We need to introduce the input signal without disturbing the bias point. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The constant voltage biasing is not a good method, 4 resistor is better. We need to introduce the input signal without disturbing the bias point. AC coupling through capacitors is used to inject ac input signal and extract output signal Capacitors provide negligible impedance at frequencies of interest and provide open circuits at dc. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The constant voltage biasing is not a good method, 4 resistor is better. We need to introduce the input signal without disturbing the bias point. AC coupling through capacitors is used to inject ac input signal and extract output signal Capacitors provide negligible impedance at frequencies of interest and provide open circuits at dc. C1 and C3 are large-valued coupling capacitors or dc blocking capacitors whose reactance at the signal frequency is designed to be negligible. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The constant voltage biasing is not a good method, 4 resistor is better. We need to introduce the input signal without disturbing the bias point. AC coupling through capacitors is used to inject ac input signal and extract output signal Capacitors provide negligible impedance at frequencies of interest and provide open circuits at dc. C1 and C3 are large-valued coupling capacitors or dc blocking capacitors whose reactance at the signal frequency is designed to be negligible. C2 is a bypass capacitor that provides a low impedance path for ac current from emitter to ground thereby removing RE from the circuit when ac signals are considered. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

DC and AC Analysis DC analysis:
Make dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Make dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model. AC analysis: Make ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. To simplify the circuit analysis and design tasks, we break the amplifier in two parts, and will do dc and ac separately. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Make dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model. AC analysis: Make ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. Replace transistor by small-signal model To simplify the circuit analysis and design tasks, we break the amplifier in two parts, and will do dc and ac separately. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Make dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model. AC analysis: Make ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. Replace transistor by small-signal model Use small-signal ac equivalent to analyze ac characteristics of amplifier. To simplify the circuit analysis and design tasks, we break the amplifier in two parts, and will do dc and ac separately. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Make dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. Find Q-point from dc equivalent circuit by using appropriate large-signal transistor model. AC analysis: Make ac equivalent circuit by replacing all capacitors by short circuits, inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. Replace transistor by small-signal model Use small-signal ac equivalent to analyze ac characteristics of amplifier. Combine end results of dc and ac analysis to yield total voltages and currents in the network. To simplify the circuit analysis and design tasks, we break the amplifier in two parts, and will do dc and ac separately. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

DC Equivalent for MOSFET Amplifier
Full circuit dc equivalent Make dc equivalent circuit by replacing all ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Full circuit dc equivalent Make dc equivalent circuit by replacing all capacitors by open circuits ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Full circuit dc equivalent Make dc equivalent circuit by replacing all capacitors by open circuits inductors by short circuits ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

AC Equivalent for MOSFET Amplifier
Full circuit dc equivalent Make ac equivalent circuit by replacing all capacitors by short circuits ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Full circuit dc equivalent Make ac equivalent circuit by replacing all capacitors by short circuits inductors by open circuits ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Full circuit dc equivalent Make ac equivalent circuit by replacing all capacitors by short circuits inductors by open circuits dc voltage sources by ground connections ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Full circuit dc equivalent Make ac equivalent circuit by replacing all capacitors by short circuits inductors by open circuits dc voltage sources by ground connections dc current sources by open circuits ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Full circuit dc equivalent Simplify the ac equivalent circuit ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

DC and AC Equivalents for MOSFET Amplifier
Full circuit dc equivalent ac equivalent Simplified ac equivalent Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

DC Equivalent for BJT Amplifier
All capacitors in original amplifier circuits need to be replaced by open circuits, disconnecting vI , RI , and R3 from circuit. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

DC Equivalent for BJT Amplifier
All capacitors in original amplifier circuits are replaced by open circuits, disconnecting vI , RI , and R3 from circuit. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

AC Equivalent for BJT Amplifier
Make ac equivalent circuit by replacing all capacitors by short circuits inductors by open circuits dc voltage sources by ground connections dc current sources by open circuits Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Simplify the ac equivalent circuit Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Modeling
For AC analysis (or general time varying analysis) we would need to use phasor , time domain, Laplace Transform (or similar) methods. Those are working better with linear systems. Need to make the linear model – small signal model. Assume that the time varying components are small signals and construct the two port model, which is linear. The concept of small signal is device dependent. We start from developing small signal model for a diode and then switch to transistor Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Operation of Diode
The slope of the diode characteristic at the Q-point is called the diode conductance and is given by: ID and VD represent the DC bias point Q-point, vD and iD are small changes around Q-point Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The slope of the diode characteristic at the Q-point is called the diode conductance and is given by: gd is small but non-zero for ID = 0 because slope of diode equation is nonzero at the origin. ID and VD represent the DC bias point Q-point, vD and iD are small changes around Q-point Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The slope of the diode characteristic at the Q-point is called the diode conductance and is given by: gd is small but non-zero for ID = 0 because slope of diode equation is nonzero at the origin. Diode resistance is given by: ID and VD represent the DC bias point Q-point, vD and iD are small changes around Q-point Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The slope of the diode characteristic at the Q-point is called the diode conductance and is given by: gd is small but non-zero for ID = 0 because slope of diode equation is nonzero at the origin. Diode resistance is given by: Thus, linear model in the vicinity of ID : when ID and VD represent the DC bias point Q-point, vD and iD are small changes around Q-point Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Model of BJT
BJT is a three terminal device and to build similar model to a diode, we would need to use 2-port y-parameter network. Using 2-port y-parameter network, The port variables can represent either time-varying part of total voltages and currents or small changes in them away from Q-point values. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small Signal Hybrid-Pi Model of BJT
The hybrid-pi small-signal model is most widely accepted model for BJT amplifier. Small-signal parameters are controlled by the Q-point Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The hybrid-pi small-signal model is most widely accepted model for BJT amplifier. Small-signal parameters are controlled by the Q-point VA - Early Voltage Trans-conductance: Input resistance: Output resistance: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The hybrid-pi small-signal model is most widely accepted model for BJT amplifier. Small-signal parameters are controlled by the Q-point VA - Early Voltage Trans-conductance: Input resistance: bo is the small-signal common-emitter current gain of the BJT. Output resistance: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The hybrid-pi small-signal model is most widely accepted model for BJT amplifier. Small-signal parameters are controlled by the Q-point VA - Early Voltage Trans-conductance: Input resistance: bo is the small-signal common-emitter current gain of the BJT. Output resistance: Definition of small signal for BJT: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Current Gain and Voltage Gain of BJT
The important small signal parameter is trans-conductance, or current-voltage (iC/vBE ) gain. It shows how the collector current changes in response to base-emitter voltage. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The important small signal parameter is trans-conductance, or current-voltage (iC/vBE ) gain. It shows how the collector current changes in response to base-emitter voltage. Other two important parameters are: - small signal current gain Small signal current gain (iC/iB = iC/(vBE /r) - gain) : In practice, however, bF and bo are often assumed to be equal. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

The important small signal parameter is trans-conductance, or current-voltage (iC/vBE ) gain. It shows how the collector current changes in response to base-emitter voltage. Other two important parameters are: - small signal current gain - intrinsic voltage gain Small signal current gain (iC/iB = iC/(vBE /r) - gain) : In practice, however, bF and bo are often assumed to be equal. Intrinsic voltage gain (vCE/vBE – gain) : For VCE << VA, mF represents maximum voltage gain individual BJT can provide, doesn’t change with operating point, and ranges from 1000 to 4000. Small signal model for pnp-BJT is similar Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Model of MOSFET (nmos)
Using 2-port y-parameter network, The port variables can represent either time-varying part of total voltages and currents or small changes in them away from Q-point values. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Model of MOSFET (nmos)
Trans-conductance: Since gate is insulated from channel by gate-oxide input resistance of transistor is infinite. Small-signal parameters are controlled by the Q-point. For same operating point, MOSFET has higher transconductance and lower output resistance that BJT. Output resistance: Amplification factor (intrinsic voltage gain) for lVDS<<1: Where l – channel-length modulation parameter. Definition of small signal for MOSFET: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Small-Signal Model of JFET

Small-Signal Model of JFET
For small-signal operation, the input signal limit is: The amplification factor is given by: Since JFET is normally operated with gate junction reverse-biased, Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Summary of FET and BJT Small-Signal Models

Common-Emitter (C-E) Amplifier
Construct AC equivalent circuit assuming Q-point is known. Input is applied to Base Output appears at Collector Emitter is common (through RE) to both input and output signal - Common-Emitter (CE) Amplifier. Developing a small signal model: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Construct AC equivalent circuit assuming Q-point is known. Use the small signal hybrid model for BJT Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Construct AC equivalent circuit assuming Q-point is known. Simplify: Use the small signal hybrid model for BJT Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-E Amplifier – Voltage Gain
Goal – develop the overall voltage gain from vi to vo - AvCE . Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Goal – develop the overall voltage gain from vi to vo - AvCE . where terminal gain - gain between transistor terminals. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Goal – develop the overall voltage gain from vi to vo - AvCE . where terminal gain - gain between transistor terminals. To find AvtCE , we connect a test source vb to the base terminal (right circuit): Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

For the input resistance RiB : Goal – develop the overall voltage gain from vi to vo - AvCE . where terminal gain - gain between transistor terminals. To find AvtCE , we connect a test source vb to the base terminal (right circuit): Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

For the input resistance RiB : We see that the overall voltage gain is the terminal gain reduced by the voltage division between R1 and equivalent resistance at the base. Thus AvtCE is the upper limit of voltage gain. Goal – develop the overall voltage gain from vi to vo - AvCE . where terminal gain - gain between transistor terminals. To find AvtCE , we connect a test source vb to the base terminal (right circuit): Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-E Amplifier - Simplifications and Limits
If we obtain the max gain: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

If we obtain the max gain: For maximum gain we set R3 >> RC and RC << rO If we assume IC RC = VCC with 0 <  < 1: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

If we obtain the max gain: For maximum gain we set R3 >> RC and RC << ro If we assume IC RC = VCC with 0 <  < 1: Typically,  = 1/3, since common design allocates one-third power supply across RC. To further account for other approximations leading to this result, we use: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

If we obtain the max gain: For maximum gain we set R3 >> RC and RC << ro If we assume IC RC = VCC with 0 <  < 1: Typically,  = 1/3, since common design allocates one-third power supply across RC. To further account for other approximations leading to this result, we use: Also, if the load resistor approaches ro (RC and R3 are very large), voltage gain is limited by amplification factor, mf , of BJT itself. For large RE, voltage gain can be approximated as: Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-E Amplifier – Example
Problem: Find voltage gain, input and output resistances. Given data: bF = 65, VA = 50 V Assumptions: Active-region operation, VBE = 0.7 V, small signal operating conditions. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

We start from finding the Q-point. DC equivalent circuit: The KVL for the input loop : The KVL for the output loop (blue): Problem: Find voltage gain, input and output resistances. Given data: bF = 65, VA = 50 V Assumptions: Active-region operation, VBE = 0.7 V, small signal operating conditions. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Next we construct the ac equivalent and simplify it. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Common-Source Amplifier
Construct AC equivalent circuit. Assume that Q-point is known. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Construct AC equivalent circuit. Assume that Q-point is known. Use the small signal hybrid model for BJT Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Construct AC equivalent circuit. Assume that Q-point is known. Simplify: Use the small signal hybrid model for MOSFET Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Construct AC equivalent circuit. Assume that Q-point is known. Simplify: Use the small signal model Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-S Amplifier - Terminal Voltage Gain
Terminal voltage gain between gate and drain: Overall voltage gain from source vi to output voltage across R3 Voltage division Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-S Amplifier - Simplifications
If we assume RI << RG Generally R3 >> RD and RD << ro. Hence, total load resistance on drain is RD. For this case, common design allocates half the power supply for voltage drop across RD and (VGS - VTN ) = 1V Also, if load resistor approaches ro, (RD and R3 are very large), voltage gain is limited by amplification factor, mf of the MOSFET itself. This implies that total signal voltage at input appears across gate-source terminals. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-S Amplifier - Input and Output Resistance
Input resistance of C-S amplifier is much larger than that of corresponding C-E amplifier. For comparable bias points, output resistances of C-S and C-E amplifiers are similar. In this case, vgs= 0. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

C-S Amplifier - Example
Do example on the board Problem: Find voltage gain, input and output resistances. Given data: Kn = 500 mA/V2, VTN = 1V, l = V-1 Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Construct dc equivalent circuit KVL: Problem: Find voltage gain, input and output resistances. Given data: Kn = 500 mA/V2, VTN = 1V, l = V-1 Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Next we construct the ac equivalent and simplify it. Topic NJIT ECE Dr. Serhiy Levkov NJIT ECE Dr. Serhiy Levkov

Summary of CE / CS Amplifiers

ECE 271 Electronic Circuits I

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ECE 271 Electronic Circuits I

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