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ECE 3336 Introduction to Circuits & Electronics General: Electronics Specific: Amplifiers Fall 2007, TUE&TH 4:00 -5:30 pm Dr. Wanda Wosik Electronics Distinction between Electrical Circuits and Electronics is somewhat artificial but quite well established.

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ece 3336 introduction to circuits electronics
ECE 3336 Introduction to Circuits & Electronics

General: Electronics

Specific: Amplifiers

Fall 2007,

TUE&TH 4:00 -5:30 pm

Dr. Wanda Wosik

  • Distinction between Electrical Circuits and Electronics is somewhat artificial but quite well established.
  • Circuits that we studied up till now were built using current and voltage sources, passive elements such as resistors but also storage elements like capacitors and inductors. Circuit theories are considered to be basic laws also for electronics.
  • So what is Electronics?


  • Electronics also deals with electrical circuits, but these circuits are made much more sophisticated than our earlier circuits. Here we are adding various active devices such as diodes and transistors.
  • These devices are then used to build even more sophisticated circuits that will then perform as elemental circuits. These new elemental circuits or chips can perform specific functions. You most probably heard about logic gates (AND, OR etc.), memories (FLASH, DRAM, SRAM etc.), or microprocessors (Intel Pentium or Core etc.). Many other circuits are being made for lots and lots of applications.
  • It looks like in electronics we are dealing with hierarchical systems constructed from simple building blocks (elemental circuits).
  • However, since in electronics we are always dealing with circuits we will rely on circuit theories while solving electronics problems.
  • Almost anywhere we look, including science and engineering, we use and take advantage of Electronics.
  • It would be difficult to list fields where electronics is not used.
application of electronics
Application of Electronics
  • Here we will be interested in using Electronics to process signals, which are applied to the circuit at its inputs. But we have been doing that throughout this course all the time! We were applying signals to the input and we were looking at the output signals. So what is the difference now?
  • There is no difference in the approach to circuit solving except that now our circuit will include new more complex building blocks such as an amplifier together with many other circuit elements that we used earlier (resistors, capacitors, inductors, sources etc).
  • We will be applying similar signals as earlier to the inputs. These signals will vary in time; they are ac signals. In general, they can be periodic steady state functions such sinusoidal waves or they can vary in time and be unpredictable as to their amplitude and phase (as real unsolicited information is delivered that way).
the role of electronics
The Role of Electronics
  • Electronic circuits are very powerful. They allow for:
    • generating signals and supplying power
    • processing signals that are applied to the circuits’ inputs by performing various analog or digital operations
      • Analog circuits deal with analog signals. Most parameters that you can measure: speed, temperature, humidity, air pressure, sound, etc. are analog. Analog signals are continuous in time. Our natural surroundings behave in an analog manner most of the time. Even some that feel like being discretized (our pulse) are in fact analog signals.
      • Digital signals are not continuous in nature. They are discrete and come as pulses or bits. Their discrete values of amplitude have assigned “1” or “0” that indicates “high” or “low”. In this course we are dealing only with analog signals.
    • converting signals to other forms. For instance in optoelectronics light can be generated or light can induce electrical signals.
  • Amplifiers are very important is processing signals by modifying (amplifying) their various parameters (amplitudes of voltage or current).
  • Amplifiers may be also specially designed to amplify power (so called power amplifiers). We say that we have power gain.
  • Special category of amplifiers will be operational amplifiers (discussed in this chapter) - they will perform various arithmetic operations on signals.
how amplifiers can do that
How Amplifiers Can Do That?
  • Amplify signals?
  • Deliver larger power than supplied by the input signal?

We can only see amplification of amplitudes or power if we balance the energy of the system. For that we have to use power supply to “empower” the amplifiers. Therefore, we have to use voltage sources.

Amplifiers use DC power supply that enables them to operate.

notation of voltages ac dc conditions
Notation of Voltages (ac, dc conditions)
  • vA total instantaneous voltage
  • VA dc component = nonvarying part of the voltage
  • va ac component = a varying part of the voltage
  • Va phasor
  • VAAPower supply, dc value, connected to a terminal.
  • Va,rms rms phasor value.

With this notation, the total voltage that has both the dc and ac components can be written: vA = VA + va.

gain is one of the most important parameters of amplifiers
Gain is One of the Most Important Parameters of Amplifiers

There are various gains that we need to describe amplifiers

Voltage gain in dB is 20(log10|Av|).

Voltage gain Av is the ratio of the voltage at the output to the voltage at the input.

Current gain Ai is the ratio of the current at the output to the current at the input.

Current gain in dB is 20(log10|Ai|).

Power gain Ap is the ratio of the power at the output to the power at the input.

Power gain in dB is 10(log10|Ap|).

basics of operational amplifiers
Basics of Operational Amplifiers

We will focus on operational amplifiers, specifically on

  • Ideal Operational Amplifiers, definitions and requirements for their ideal operation
  • Negative Feedback that allows for op-amp to be controlled by external elements
operational amplifiers op amps
Operational Amplifiers (Op Amps)
  • Op-amps behave as ideal elements, whose behavior in circuits can be accurately predicted.
  • Generic function of op-amps is to amplify voltages.
  • But their operation can be determined rather by external elements connected to the op-amps than by the op-amps. How and what we use as external elements determine what operations and functions op-amps can perform in the circuits.
  • Due to their very high versatility in operation, op-amps have very wide applications in electronics.
concept of op amps
Concept of Op-amps

Voltage at the output is obtainedwith respect to a reference (ground). That creates a single ended output.

The differential input indicates a voltage difference applied between the input terminals. These inputs are called inverting and noninverting


Inverting input



Noninverting input

op amps have to have power supply for operation
Op Amps Have to Have Power Supply for Operation

Operation of op-amps requires power supply. So there are symmetrical dc voltage sources that are used in op-amps (frequently ±15V). Op-amps are made as ICs. Pins contacting various nodes (inputs, output, supply voltages etc.) are shown below.

Negative dc

power supply






Positive dc

power supply

bipolar integrated circuit op amp
Bipolar Integrated Circuit Op-Amp

Positive dc power supply

Bipolar transistors are used for building an op-amp

There are other op-amp designs where MOS transistors are used.

Negative dc power supply

equivalent schematic of op amps
Equivalent Schematic of Op Amps

Equivalent circuit of the op amp includes

  • the differential voltageapplied at the two inputs,
  • a dependent source amplifying the differential input signal by a large amount, AV(OL)
  • input resistance of a very large value (because )
  • output resistance (small value); this resistance can be frequently ignored.


Equivalent Circuit for the Op Amp

Voltage gain

common mode rejection in op amps
Common Mode Rejectionin op-amps

The output voltage should be ZERO volts for v-= v+ i.e. vin=0V.


This is called common mode rejectioni.e. common or the same voltages will not be amplified despite a very large voltage gain AV(OL) in the open loop (OL) op-amp..

But op-amps are not perfectly symmetrical and some signal at the output may appear. We will talk (later) about the common mode rejection ratio to describe this effect.


Equivalent Circuit for the Op Amp


Op Amps: The Gain

  • The dependent source is determined by the gain of op-amp (called differential gain).
  • This gain, AV(OL)is very large (105-107) in the open loop configuration.
  • The gain AV(OL) is a decreasing function of frequency, however. We will see later that capacitive parasitics will lower this high gain when frequency increases.

Saturation ≈V+



High Slope

AV(OL) large


Saturation ≈V-


Op Amps: Saturation

The maximum positive value of the output voltage is limited by thepositivedc power supply voltage(V+) and the minimum voltage is limited by the negativedc power supply (V-). This restrictions impose limits on the input voltage, which for the open look configuration, cannot be small enough to avoidsaturation. We will always see saturation in the open loop configuration.


Saturation ≈V+


High Slope

AV(OL) large


Saturation ≈V-

solving op amp circuits
Solving Op Amp Circuits

There are two assumptions important while analyzing and designing op amp circuits. We will call them golden rules and we will use them always whenever the op amps can be treated as ideal elements.

The first assumption:

i- = i+ = 0

results from large resistances at the input. Currents do not flow into the op-amp.

The second assumption:


deals with the output that makes the input voltages equal v+≈v-. This is realized by introducing a negative feedback loop, which will span the output and the inverting input.


negative feedback loop

a note on the second assumption
A note on the Second Assumption

The second golden rule v- = v+results in the virtual short, or the summing-point constraint. The constrain refers to the input voltages, which become the same if there is a negative feedback and the open loop gain Av(OL) is large.

Without negative feedback, even a small input voltage will cause saturation of the output either at V+ or V-.

Negative dc

power supply







This is open loop configuration

+ dc V supply

negative feedback
Negative Feedback

Engineers have developed a way of looking at signals called the signal flow diagram. This is not a schematic, and does not represent wire and specific components. A line represents a path that a signal might follow. The signals can be voltages or currents. Therefore, we will label the signals with the symbol x.

In the signal flow diagram shown below, there is an input signal, xi. This signal flows into an amplifier with gain A, which is shown with a triangle. This produces an output signal xo. The input is multiplied by the gain, to give the output.


Signal Flow Diagram

Feedback notes were developed by Dr. Shattuck

negative feedback signal flow diagrams
Negative Feedback – Signal Flow Diagrams

Now, let’s add negative feedback to our signal flow diagram. In the signal flow diagram shown below, we add another amplifier. This amplifier has a gain which is conventionally called b. This amplifier amplifies the output signal, to produce a feedback signal, xf. Finally, this feedback signal is subtracted from the input signal. The symbol for this action is called a summing point or a summing junction. The signs  at the junction indicate the signs for the summation.

summing point

subtracted from the input signal

negative feedback

negative feedback definition
Negative Feedback – Definition

At this point, we can define negative feedback. Negative feedback is when a portion of the output is taken, returned to the input, and subtracted from this input.

If we were to add it to the input, we would call it positive feedback.


negative feedback notes
Negative Feedback – Notes

The feedback amplifier, with a gain of b, is typically not an amplifier per se, but rather is a passive (resistive) network. The key is that the feedback signal xf is proportional to the output signal, with a multiplier equal to b.

The gain A is called the open loop gain (our AV(OL)), because this would be the gain if the loop were to be opened, that is, if the feedback were removed.

gain with negative feedback
Gain with Negative Feedback

The input signal, which includes -ve feedback gain 

Now, let’s solve for the gain with negative feedback, which is xo/xs. We start by writing an equation for the summing junction, taking into account the signs, to get

Next, we use a similar definition for the feed-forward gain, A, to write


We then substitute the first equation into the second to get

Open loop

We can combine terms, then we can divide through by xs, and then by (1+Ab), to get

Feedback loop

gain with negative feedback26
Gain with Negative Feedback

This is the gain with negative feedback (a closed loop gain)

If we take the case where A is very large, and it usually is, we can get a special situation. Specifically, take the case where Ab >> 1. Then,

and we can use this approximation to simplify the gain with feedback, which we call Af, to

gain with negative feedback27
Gain with Negative Feedback

Thus, the gain with negative feedback, Af, is

The onlyrequirement is that Ab >> 1. Thus, the gain is not a function of A at all !?!This is a seemingly bizarre, but wondrous result, which is fundamental to the power of negative feedback.

The gain of the op amp, which changes from time to time, and from op amp to op amp, does not affect the overall gain with feedback.

gain with negative feedback28
Gain with Negative Feedback

Important, so it is repeated again: The gain with negative feedback, Af, is

  • Thus, the gain is not a function of A at all!?! The gain of the op amp does not affect the overall gain with feedback. The overall gain, Af, is determined by the way feedback is applied.
  • Feedback is used to allow gain to be traded off for a variety of desirable results. When we use op amps, we have a relatively simple way to determine the presence of negative feedback:
    • If there is a signal path between the output of the op amp, andthe inverting input, there will be negative feedback.
gain with negative feedback29
Gain with Negative Feedback

With this result, we can look again at the signal flow diagram. The input to the op amp, vi, is the outputdivided by the gain, vo/A. If A is large, then viwill be much less than vo, and can usually be neglected. Neglect the input?No -neglect the differential signal at the input vi!

vi=vo/A vi≈0V

So we have our second golden rule v+=v-

Thus, the gain with negative feedback, Af, is

This is what we call the virtual short.

consequences of negative feedback
Consequences of Negative Feedback.
  • The two assumptions or our golden rules will be now used to solve op amp circuits much more easily.
  • All that we need is an ideal op-amp
    • high input resistance
    • large open loop gain and
  • Negative feedback.

In op-amps we also can have a feedback loop that would span an output and the noninverting input. This will be called Positive feedback, which is also very useful for some applications. However, we will stay with negative feedback loops in our circuits. Always verify that there is a loop like that in your circuit.

op amp circuits with the negative feedback loop
Op Amp Circuits with the Negative Feedback Loop

Negative feedback adds a portion of the output signal to the inverting input. Since the signs of these voltages are opposite, the negative feedback acts as if the signal applied to the input decreases.

The net result is that the output voltage can be controlled by the external elements and does not saturate.

Negative feedback

If assumptions that the op-amp is ideal (most of the times) are true we will apply two golden rules to solve circuits


Golden Rules

1)i- = i+ = 0.

2) v- = v+. Virtual short

op amp in inverting configuration
Op Amp in Inverting Configuration

An op amp operates in the inverting configuration when the input voltage is applied to the inverting terminal.

RF is the feedback resistor

Rs is the source resistor

There is a negative feedback loop on RF

That assures that we have the virtual short:v-=v+. Since v+=0V also v-=0V.

The op-amp does not draw currents iin=0A



solving op amp in the inverting configuration closed loop
Solving op-amp in the Inverting ConfigurationClosed Loop

To find vout we have to find vRF.

To find vRF we have to know current iF which can be calculated from is.

The current is is given by the voltage Vs and Rs.

If we have golden rules (iin=0, v+=v-)


Closed loop voltage GAIN:

verify if we really have the virtual short



Verify if we Really Have the Virtual Short






When you look at the currents it will be obvious that is flows in the same direction as iF.

So if you choose is=iF to calculate vout you would use vout=-iFRF. The result will be the same as before *


Virtual ground

Virtual short

significance of the gain calculation
Significance of the Gain Calculation

The negative feedback loop, combined with the ideal properties of the op-amp (high open loop gain 105-107 and large input resistance) ensures that

  • the gain does not depend on the op amp
  • the gain is the determined by a ratio of two resistors connected to the op-amp.
consequences of the negative feedback
Consequences of the Negative Feedback
  • Negative feedback prevents output saturation for small input signals. Our first case of inverting configuration is illustrated below. Note that the phase is indeed inverted for the output signal.
  • We will use negative feedback loop in many applications of op-amp.
the summing amplifier
The Summing Amplifier
  • We use the same golden rules as before since we have a negative feedback loop and the amplifier is assumed to be ideal:
    • iin=0
    • v+=v-


n=1, 2, …, N

The virtual short results in virtual ground at the inverting input.

The voltage at the output is inverted in phase and includes voltage sources weighted by a ratio of resistors