Project Report 2011

Table of Contents

i) Amplifiers……….………………………………………………………………02

ii) Ideal amplifier……………………….………………………………………….03

iii) An introduction to the operational amplifier………………….……………...04(1) Ideal characteristics.

……………………………………………………………..05(2) Practical characteristics………………………..…………………….

………………06iv) Limitations of the op-amp……………………………………..………………

06v) Applications of OP-AMPS……………………………………..

……………...06(1) As an

Integrator……………………………………………………………………07

(2) As a Differentiator………………………………………………………………..10

(3) As an Inverter………………………………………………………………………13

vi) As a Comparator…………………….…………………………………………17

vii) Overview of uA741 ……………………………………………………………18

viii) Given Task……………………………………………………………………...20

ix) Problems regarding Project and their Solutions……………………………20

x) Future Direction………………………………………………………………...23

xi) References……………………………………………………………………...24

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Amplifiers

In "Electronics", signal amplifiers are widely used devices as they have the ability to amplify a relatively small input signal, for example from a Sensor such as a microphone, into a much larger output signal to drive a Relay, lamp or loudspeaker There are many forms of electronic circuits classed as amplifiers.

Amplifiers can be thought of as a simple box or block containing the amplifying device, such as a Transistor, Field Effect Transistor or Op-amp, which has two input terminals and two output terminals (ground being common) with the output signal being much greater than that of the input signal as it has been "Amplified”. An ideal amplifier has three main properties, Input Resistance or ( Rin ), Output Resistance or ( Rout ) and of course amplification known commonly as Gain or ( A ). No matter how complicated an amplifier circuit is, a general amplifier model can be used to show the relationship of these three properties.

Amplifier Gain

Then the gain of an amplifier can be said to be the relationship that exists between the signals measured at the output with the signal measured at the input. There are

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three different kinds of Amplifier Gain, Voltage Gain, ( Av ), Current Gain ( Ai ) and Power Gain ( Ap ) and examples of these are given below.

Amplifier Gain of the Input Signal

Voltage Amplifier Gain

Current Amplifier Gain

Power Amplifier Gain

Amplifier Efficiency

Ideal Amplifier

We can know specify the characteristics for an ideal amplifier from our discussion above with regards to its Gain, meaning voltage gain:

1. The amplifiers gain, ( A ) should remain constant for varying values of input signal.

2. Gain is not be affected by frequency. Signals of all frequencies must be amplified by exactly the same amount.

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3. The amplifiers gain must not add noise to the output signal. It should remove any noise that is already exists in the input signal.

4. The amplifiers gain should not be affected by changes in temperature giving good temperature stability.

5. The gain of the amplifier must remain stable over long periods of time.

An Introduction to the Operational Amplifier

An operational amplifier IC is a solid-state integrated circuit that uses external feedback to control its functions. It is one of the most versatile devices in all of electronics.

The term 'op-amp' was originally used to describe a chain of high performance dc amplifiers that was used as a basis for the analog type computers of long ago. The very high gain op-amp IC's our days uses external feedback networks to control responses. The op-amp without any external devices is called 'open-loop' mode, referring actually to the so-called 'ideal' operational amplifier with infinite open-loop gain, input resistance, bandwidth and a zero output resistance.

Operational amplifiers are linear devices that have all the properties required for

nearly ideal DC amplification and are therefore used extensively in signal

conditioning, filtering or to perform mathematical operations such as add, subtract,

integration and differentiation. An ideal Operational Amplifier is basically a three-

terminal device which consists of two high impedance inputs, one called the

Inverting Input, marked with a negative sign, ("-") and the other one called the Non-

inverting Input, marked with a positive plus sign ("+").

The third terminal represents the op-amps output port which can both sink and

source either a voltage or a current. In a linear operational amplifier, the output

signal is the amplification factor, known as the amplifiers gain (A) multiplied by the

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value of the input signal and depending on the nature of these input and output

signals

Equivalent Circuit for Ideal Operational Amplifiers

Op-amp Idealized CharacteristicsPARAMETER IDEALIZED CHARACTERISTIC

I. Open Loop Gain, (Avo)

Infinite - The main function of an operational amplifier is to amplify the input signal and the more open loop gain it has the better. Open-loop gain is the gain of the op-amp without positive or negative feedback and for an ideal amplifier the gain will be infinite but typical real values range from about 20,000 to 200,000. 

II. Input impedance, (Zin)

Infinite - Input impedance is the ratio of input voltage to input current and is assumed to be infinite to prevent any current flowing from the source supply into the amplifiers input circuitry (Iin =0). Real op-amps have input leakage currents from a few pico-amps to a few milli-amps. 

III. Output impedance, (Zout)

Zero - The output impedance of the ideal operational amplifier is assumed to be zero acting as a perfect internal voltage source with no internal resistance so that it can supply as much current as necessary to the load. This internal resistance is effectively in series with the load thereby reducing the output voltage available to the load. Real op-amps have output-impedance in the 100-20Ω range. 

IV. Bandwidth, (BW) Infinite - An ideal operational amplifier has an infinite frequency response and can amplify any frequency signal from DC to

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the highest AC frequencies so it is therefore assumed to have an infinite bandwidth. With real op-amps, the bandwidth is limited by the Gain-Bandwidth product (GB), which is equal to the frequency where the amplifiers gain becomes unity. 

V. Offset Voltage, (Vio) Zero - The amplifiers output will be zero when the voltage difference between the inverting and the non-inverting inputs is zero, or inputs are grounded.

Op-amp Practilized CharacteristicsPARAMETER PRACTILIZED CHARACTERISTIC

I. Open Loop Gain, (Avo) : HighII. Input impedance, (Zin): High

III. Output impedance, (Zout): LowIV. Bandwidth, (BW): HighV. Offset Voltage, (Vio): Low

Limitations of Op-amp

Some of the limitations that an operational amplifier has are listed below:

1. Use of two additional batteries2. Operative on low frequencies3. Gain is limited 4. The input current isn't exactly zero. 5. The input offset current isn't exactly zero either. 6. The input impedance isn't infinite. 7. There is a limited common mode voltage range. 8. The output impedance isn't zero. 9. There are voltage gain limitations including phase shifts. 10.There is a finite input offset voltage. 11.There is a finite slew rate. 12.There is some temperature dependence. 13.They are not the power amplifier.

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Applications of the Op-amp

Operational amplifier is used widely in many applications such as:

A. IntegratorB. DifferentiatorC. InverterD. Comparator

As an Integrator:

The integrator does just what the name implies. It integrates - in the calculus sense - the input signal to produce the output signal. There is a scaling factor and a minus sign again, but that's pretty much what happens.

Here's the analysis. We make the usual assumptions:

V- = 0

We assume that the input voltage at the inverting input is a virtual ground.

We assume that no current enters the input terminals of the op-amp.

Then, we have - after we write KCL:

C(dVout/dt) + V1/R = 0

C(dVout/dt) + V1/R = 0

Then:

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Integrator Amplifier Circuit

As its name implies, the Integrator Amplifier is an operational amplifier circuit that performs the mathematical operation of Integration that is we can cause the output to respond to changes in the input voltage over time. The integrator amplifier acts like a storage element that

"PRODUCES A VOLTAGE OUTPUT WHICH IS PROPORTIONAL TO THE INTEGRAL OF ITS INPUT VOLTAGE WITH RESPECT TO TIME".

In other words the magnitude of the output signal is determined by the length of time a voltage is present at its input as the current through the feedback loop charges or discharges the capacitor as the required negative feedback occurs through the capacitor.

When a voltage, Vin is firstly applied to the input of an integrating amplifier, the uncharged capacitor C has very little resistance and acts a bit like a short circuit (voltage follower circuit) giving an overall gain of less than one. No current flows into the amplifiers input and point X is a virtual earth resulting in zero output. As the feedback capacitor C begins to charge up, its reactance Xc decreases this results in the ratio of Xc/Rin increasing producing an output voltage that continues to increase until the capacitor is fully charged.

At this point the capacitor acts as an open circuit, blocking anymore flow of DC current. The ratio of feedback capacitor to input resistor (Xc/Rin) is now infinite resulting in infinite gain. The result of this high gain (similar to the op-amps open-loop gain), is that the output of the amplifier goes into saturation as shown below. (Saturation occurs when the output voltage of the amplifier swings heavily to one voltage supply rail or the other with little or no control in between).

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The rate at which the output voltage increases (the rate of change) is determined by the value of the resistor and the capacitor, "RC time constant". By changing this RC time constant value, either by changing the value of the Capacitor, C or the Resistor, R, the time in which it takes the output voltage to reach saturation can also be changed for example.

If we apply a constantly changing input signal such as a square wave to the input of an Integrator Amplifier then the capacitor will charge and discharge in response to changes in the input signal. This results in the output signal being that of a saw tooth waveform whose frequency is dependent upon the RC time constant of the resistor/capacitor combination. This type of circuit is also known as a Ramp Generator and the transfer function is given below.

Ramp Generator

We know from first principals that the voltage on the plates of a capacitor is equal to the charge on the capacitor divided by its capacitance giving Q/C. Then the voltage across the capacitor is output Vout therefore: -Vout = Q/C. If the capacitor is charging and discharging, the rate of charge of voltage across the capacitor is given as:

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But dQ/dt is electric current and since the node voltage of the integrating op-amp at its inverting input terminal is zero, X = 0, the input current I(in) flowing through the input resistor, Rin is given as:

The current flowing through the feedback capacitor C is given as:

Assuming that the input impedance of the op-amp is infinite (ideal op-amp), no current flows into the op-amp terminal. Therefore, the nodal equation at the inverting input terminal is given as:

From which we derive an ideal voltage output for the Integrator Amplifier as:

To simplify the math's a little, this can also be re-written as:

Where jω = 2πƒ and the output voltage Vout is a constant 1/RC times the integral of the input voltage Vin with respect to time. The minus sign (-) indicates an 180o

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phase shift because the input signal is connected directly to the inverting input terminal of the op-amp.

As a Differentiator

Differentiator is exact opposite to the Integrator, as the position of the capacitor and resistor have been reversed and now the reactance, Xc is connected to the input terminal of the inverting amplifier while the resistor, Rf forms the negative feedback element across the operational amplifier as normal.

This circuit performs the mathematical operation of Differentiation that is it "PRODUCES A VOLTAGE OUTPUT WHICH IS DIRECTLY PROPORTIONAL TO THE INPUT VOLTAGE'S RATE-OF-CHANGE WITH RESPECT TO TIME".

In other words the faster or larger the change to the input voltage signal, the greater the input current, the greater will be the output voltage change in response, becoming more of a "spike" in shape.

As with the integrator circuit, we have a resistor and capacitor forming an RC Network across the operational amplifier and the reactance (XC) of the capacitor plays a major role in the performance of a Differentiator Amplifier.

Differentiator Amplifier Circuit

The input signal to the differentiator is applied to the capacitor. The capacitor blocks any DC content so there is no current flow to the amplifier summing point, X resulting in zero output voltage. The capacitor only allows AC type input voltage changes to pass through and whose frequency is dependent on the rate of change of the input signal. At low frequencies the reactance of the capacitor is "High" resulting in a low gain (Rf/Xc) and low output voltage from the op-amp. At higher frequencies the reactance of the capacitor is much lower resulting in a higher gain and higher output voltage from the differentiator amplifier.

However, at high frequencies a differentiator circuit becomes unstable and will start to oscillate. This is due mainly to the first-order effect, which determines the frequency response of the op-amp circuit causing a second-order response which,

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at high frequencies gives an output voltage far higher than what would be expected. To avoid this high frequency gain of the circuit needs to be reduced by adding an additional small value capacitor across the feedback resistor Rf.

Ok, some math's to explain what's going on! Since the node voltage of the operational amplifier at its inverting input terminal is zero, the current, i flowing through the capacitor will be given as:

The charge on the capacitor equals Capacitance x Voltage across the capacitor

The rate of change of this charge is

But dQ/dt is the capacitor current i

From which we have an ideal voltage output for the Differentiator Amplifier is given as:

Therefore, the output voltage Vout is a constant -Rf.C times the derivative of the input voltage Vin with respect to time. The minus sign indicates a 180o phase shift because the input signal is connected to the inverting input terminal of the operational amplifier.

One final point to mention, the Differentiator Amplifier circuit in its basic form has two main disadvantages compared to the previous integrator circuit. One is that it suffers from instability at high frequencies as mentioned above, and the other is that the capacitive input makes it very susceptible to random noise signals and any C

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noise or harmonics present in the source circuit will be amplified more than the input signal itself. This is because the output is proportional to the slope of the input voltage so some means of limiting the bandwidth in order to achieve closed-loop stability is required.

Differentiator Waveforms

If we apply a constantly changing signal such as a Square-wave, Triangular or Sine-wave type signal to the input of a differentiator amplifier circuit the resultant output signal will be changed and whose final shape is dependent upon the RC time constant of the Resistor/Capacitor combination.

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As an Inverter

The triangular gain block symbol is again used to represent an ideal op amp. The input terminal, + (Vp), is called the non-inverting input, whereas – (Vn) marks the inverting input. It is similar to the non-inverting circuit shown in Figure 4 except that

Now the signal is applied to the inverting terminal via R1 and the non-inverting terminal is grounded.

An op amp can produce a signal which is 180 degrees out of phase (inverted) with respect to the input signal. To use an op amp as an inverting amplifier, send the signal into the negative input instead of the positive input. As the op amp will do everything it possibly can to make the voltage (signal) on the negative input match the positive input. In the following diagram, that the positive input is connected to ground. It's shown as being connected through a resistor but the resistance to ground in unimportant. What is important is that the positive input has no signal (it's connected to the reference, ground). This means that the op amp's negative input will have no visible (voltage) signal on it. When you're driving the negative input it will act as a virtual ground. The input is converted from a voltage drive to a current drive. The change in current is what drives the op amp. This is important to know because at the negative input with an oscilloscope, no signal (when the circuit is an inverting amplifier). The op amp inputs had very high impedance. While this is true, when using the inverting input with feedback (which is necessary for audio reproduction), the input impedance becomes the value of the input resistor.

Calculating Voltage Gain (inverting input):

By knowing the value of the feedback, inverting input resistor and input voltage, we can calculate the output voltage. The formula is:

Vout = Vin*(Rf/Ri)*-1

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Inverting Amplifier Configuration

In this Inverting Amplifier circuit the operational amplifier is connected with feedback to produce a closed loop operation. For ideal op-amps there are two very important rules to remember about inverting amplifiers, these are: "no current flows into the input terminal" and that "V1 equals V2", (in real op-amps both these rules are broken). This is because the junction of the input and feedback signal (X) is at the same potential as the positive (+) input which is at zero volts or ground then, the junction is a "Virtual Earth". Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor, Rin and the closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors.

We said above that there are two very important rules to remember about Inverting Amplifiers or any operational amplifier for that matter and these are.

1.  No Current Flows into the Input Terminals 

2.  The Differential Input Voltage is Zero as V1 = V2 = 0 (Virtual Earth)

Then by using these two rules we can derive the equation for calculating the closed-loop gain of an inverting amplifier, using first principles.

Current ( i ) flows through the resistor network as shown.

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Then, the Closed-Loop Voltage Gain of an Inverting Amplifier is given as.

And this can be transposed to give Vout as:

LINEAR OUTPUT

The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180o out of phase. This is due to the feedback being negative in value.

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The equation for the output voltage Vout also shows that the circuit is linear in nature for a fixed amplifier gain as Vout = Vin x Gain. This property can be very useful for converting a smaller sensor signal to a much larger voltage.

As a Comparator

The operational amplifier was originally developed for analogue computing (our PCs are digital computers) and when introduced were complex and expensive components.  Now they are in integrated circuit form and are very cheap, about 50 p (0.7 Euros).  They are not very spectacular, but are extremely useful.

A comparator compares two input voltages. These are usually a reference voltage and a signal from a sensor. The output switches state when the signal input crosses the reference voltage.

THE COMPARATOR RELIES ON THE VERY HIGH OPEN LOOP GAIN OF THE OP' AMP'. VERY SMALL CHANGES IN THE INPUT CAUSE THE OP AMP TO SATURATE SO THE OUTPUT IS ALWAYS LOW OR HIGH AND ALMOST NEVER UNDECIDED.For a real-life op' amp' this gain will be between 105 and 107.This means that a potential difference between V1 and V2 of only a few micro volts is sufficient to saturate the op' amp'.

If V1 is greater than V2 then Vout will go high (close to the + supply voltage)If V1 is less than V2 then Vout will go low (close to the - supply voltage).

Operational amplifiers require a dual power supply, which means having a central 0 volts rail, and a + 15 V rail and a – 15 V rail. The full circuit diagram is shown below, but generally we will ignore the power supply.

 

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Notice that the op-amp has two inputs and one output.  It amplifies the difference between the inverting input and non-inverting input.  Be careful not to confuse the symbol with a non-inverting gate. 

Overview of the uA741

Of the different types of op – amps produced, type 741 has achieved a very wide popularity. It is available in 14- pin dual-in line, 8 – pin dual-in line or in TO- style packages. Integrated circuit type 747 accommodates two type 741 operational amplifiers in a single package.

uA 741 various package styles:

Definition of 741-pin functions:

1. Pin 1 (Offset Null): Since the op-amp is the differential type, input offset voltage must be controlled so as to minimize offset. Offset voltage is nulled by application of a voltage of opposite polarity to the offset. An offset null-adjustment potentiometer may be used to compensate for offset voltage. The null-offset potentiometer also compensates for irregularities in the operational amplifier manufacturing process which may cause an offset. Consequently, the null potentiometer is recommended for critical applications. See 'Offset Null Adjustment' for method.

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2. Pin 2 (Inverted Input): All input signals at this pin will be inverted at output pin 6. Pins 2 and 3 are very important (obviously) to get the correct input signals or the op amp cannot do its work.

3. Pin 3 (Non-Inverted Input): All input signals at this pin will be processed normally without inversion. The rest is the same as pin 2.

4. Pin 4 (-V): The V- pin (also referred to as Vss) is the negative supply voltage terminal. Supply-voltage operating range for the 741 is -4.5 volts (minimum) to -18 volts (max), and it is specified for operation between -5 and -15 Vdc. The device will operate essentially the same over this range of voltages without change in timing period. Sensitivity of time interval to supply voltage change is low, typically 0.1% per volt. (Note: Do not confuse the -V with ground).

5. Pin 5 (Offset Null): See pin 16. Pin 6 (Output): Output signal's polarity will be the opposite of the input's

when this signal is applied to the op-amp's inverting input. For example, a sine-wave at the inverting input will output a square-wave in the case of an inverting comparator circuit.

7. Pin 7 (posV): The V+ pin (also referred to as Vcc) is the positive supply voltage terminal of the 741 Op-Amp IC. Supply-voltage operating range for the 741 is +4.5 volts (minimum) to +18 volts (maximum), and it is specified for operation between +5 and +15 Vdc. The device will operate essentially the same over this range of voltages without change in timing period. Actually, the most significant operational difference is the output drive capability, which increases for both current and voltage range as the supply voltage is increased. Sensitivity of time interval to supply voltage change is low, typically 0.1% per volt.

8. Pin 8 (N/C): The 'N/C' stands for 'Not Connected'. There is no other explanation. There is nothing connected to this pin, it is just there to make it a standard 8-pin package.

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Keep this in mind as a rule-of-thumb:

An operational amplifier circuit will not work at all unless:

1. External feedback limits the gain or desired response to a design value.

2. Both inputs have direct-current return path to ground of a similar reference.

3. The input frequencies and required gain are well within the performance limitations of the op-amp used.

Given Task:

We are given to desing an operational amplifier having following specifications such as:

All the circuits’ i.e. operational amplifier as an integrator, an inverter, a differentiator, and as a comparator should …

a) Use single IC 741 for all the 4 circuitsb) Use switches to ON just one single at a timec) Single input supply

Problems and their solutions

Some of the problems we faced during our project are listed below:

I. Complexity of the practically design circuitII. Compiling of a circuit

III. Use of the switches

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IV. Isolation the input supply

We have overcome on these problems as:

Complexity of the practically design circuits:

Ideally the all the circuits are grounded at the non-inverting terminal (03) but practically we use respective resistances across it to avoid… that makes the circuit complex

Solution:

To make the circuit practically efficient it is recommended to use these resistances rather than being it grounded

Compiling of the circuit:

To achieve the task, all the circuits should be complied up on a single overboard using IC.

Solution:

For this we design circuit by our self shown below:

Circuit design by the Group Members

BS.(Hons.) 4th Semester

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Use switches:

We are assigned to use switches to ON the one circuit at a time

Solution:

We use switches separately for all the circuits at inverting terminal (02) , as the input is supplied to all circuit through inverting terminal, than by the help of the switches we allowed input signal to pass through a selected portion of the circuit

Isolation of the circuit:

Input supply can isolated

Solution:

Circuit design by the Group Members

BS.(Hons.) 4th Semester

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For this we have to use some of the extra switches at the input supply to the inverting terminal that isolates the input supply.

Future Directions:

To get more efficient result w can alter the following specifications as:

1. We can use less switches up to just 4 If we does not isolates the input supply 2. For avoid any damage to the LED we can use another resistance at the

output terminal of almost 1K.3. We can use more practically effiecnt circuits design.

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References

1) www.amplifiercircuits.com ………………………………..26-05-112) www.antonnie-education.co.edu ..………………………15-06-113) www.bcae1.com .……………………….…………………..14-06-114) www.brown.edu …………………………………………...14-06-115) www.bucknell.edu ………..…………………………….....14-06-116) www.circuitstoday.com ……………………………………15-06-117) www.electronicstutorial.com ……………………………..14-06-118) www.forumer.com …………….……….…………………..14-06-119) www.hamradioindia.com …………….……………………15-06-1110)Handbook of Operational amplifier applications by Thomas

R .Brown J………………………………..………………...…31-05-11

11)www.hyperphyscis.com ……………..……………………14-06-1112)Mixed signal and analogue operational amplifier by Jim

Karki(1988)………………………………………………….31-05-1113)www.sentex.net ……………………………………………15-06-1114)www.softwarefrodeucation.com ………………………….14-06-1115)www.swarthmore.edu ……………….…………………….14-06-11

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