Signal Amplification, Attenuation, Integration, Differentiation, Wave Shaping

Signal amplification:

Signal amplification is carried out when the typical signal output level of a measurement transducer is considered to be too low. Amplifiecation by analogue means is carried out by an operational amplifier. This is normally required to have a high input impedance so that its loading effect on the transducer output signal is minimized. In some circumstances, such as when amplifying the output signal from accelerometers and some optical detectors, the amplifiermust also have a high-frequency response, to avoid distortion of the output reading. Thus,To drive the output of stages of the instrumentation system, the direct output of the transducer is not capable . So, the strength of the weak signal is to be increased. This boosting function is done by the Signal amplifier . In Instrumentation system, op-amp based amplifiers are used. Some of the important amplifiers constructed using op-amps are listed below:

1. Inverting amplifier
2. Non-inverting amplifier
3. Buffer amplifier
4. Differential amplifier
5. Summing amplifier
6. Instrumentation amplifier
7. Integrator amplifier
8. Subtractor(difference) amplifier and so on

They are explained briefly below:

1.Inverting amplifier:

In this Inverting Amplifiercircuit the operational amplifier is connected with feedback to produce a closed loop operation. When dealing with operational amplifiers there are two very important rules to remember about amplifiers, these are:“No current flows into the input terminal”and that“V1 always equals V2”. However, in real world op-amp circuits both of these rules are slightly 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 ,Rinand 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 aboutInverting Amplifier or any operational amplifier for that matter and these are.

• No Current Flows into the Input Terminals
• 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.

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

and this can be transposed to give Vout as:

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

2.Non-inverting Operational Amplifier

The second basic configuration of an operational amplifier circuit is that of aNon-inverting Operational Amplifier. In this configuration, the input voltage signal, (Vin) is applied directly to the non-inverting (+) input terminal which means that the output gain of the amplifier becomes “Positive” in value in contrast to the “Inverting Amplifier” circuit we saw in the last tutorial whose output gain is negative in value. The result of this is that the output signal is “in-phase” with the input signal.

Feedback control of the non-inverting operational amplifier is achieved by applying a small part of the output voltage signal back to the inverting (–) input terminal via aRƒ – R2voltage divider network, again producing negative feedback. This closed-loop configuration produces a non-inverting amplifier circuit with very good stability, a very high input impedance,Rinapproaching infinity, as no current flows into the positive input terminal, (ideal conditions) and a low output impedance,Routas shown below.

In the previous Inverting amolifiertutorial, we said that for an ideal op-amp“No current flows into the input terminal”of the amplifier and that“V1 always equals V2”. This was because the junction of the input and feedback signal (V1) are at the same potential.

In other words the junction is a “virtual earth” summing point. Because of this virtual earth node the resistors,RƒandR2form a simple potential divider network across the non-inverting amplifier with the voltage gain of the circuit being determined by the ratios ofR2andRƒas shown below.

Equivalent Potential Divider Network

Then using the formula to calculate the output voltage of a potential divider network, we can calculate the closed-loop voltage gain (A_V) of theNon-inverting Amplifier as follows:

Voltage Follower (Unity Gain Buffer)

If we made the feedback resistor,Rƒequal to zero, (Rƒ=0), and resistorR2equal to infinity, (R2=∞), then the circuit would have a fixed gain of “1” as all the output voltage would be present on the inverting input terminal (negative feedback). This would then produce a special type of the non-inverting amplifier circuit called aVoltage Followeror also called a “unity gain buffer”.As the input signal is connected directly to the non-inverting input of the amplifier the output signal is not inverted resulting in the output voltage being equal to the input voltage,Vout = Vin. This then makes thevoltage followercircuit ideal as a Unity gain buffercircuit because of its isolation properties.

The advantage of the unity gain voltage follower is that it can be used when impedance matching or circuit isolation is more important than amplification as it maintains the signal voltage. The input impedance of the voltage follower circuit is very high, typically above 1MΩ as it is equal to that of the operational amplifiers input resistance times its gain (RinxAo). Also its output impedance is very low since an ideal op-amp condition is assumed.

In this non-inverting circuit configuration, the input impedanceRinhas increased to infinity and the feedback impedanceRƒreduced to zero. The output is connected directly back to the negative inverting input so the feedback is 100% andVinis exactly equal toVoutgiving it a fixed gain of1or unity. As the input voltageVinis applied to the non-inverting input the gain of the amplifier is given as:

Since no current flows into the non-inverting input terminal the input impedance is infinite (ideal op-amp) and also no current flows through the feedback loop so any value of resistance may be placed in the feedback loop without affecting the characteristics of the circuit as no voltage is dissipated across it, zero current flows, zero voltage drop, zero power loss.Since the input current is zero giving zero input power, the voltage follower can provide a large power gain. However in most real unity gain buffer circuits a low value (typically 1kΩ) resistor is required to reduce any offset input leakage currents, and also if the operational amplifier is of a current feedback type.

The voltage follower or unity gain buffer is a special and very useful type ofNon-inverting amplifier circuit that is commonly used in electronics to isolated circuits from each other especially in High-order state variable or Sallen-Key type active filters to separate one filter stage from the other. Typical digital buffer IC’s available are the 74LS125 Quad 3-state buffer or the more common 74LS244 Octal buffer.One final thought, the closed loop voltage gain of a voltage follower circuit is “1” orUnity. The open loop voltage gain of an operational amplifier with no feedback isInfinite. Then by carefully selecting the feedback components we can control the amount of gain produced by a non-inverting operational amplifier anywhere from one to infinity.

3.The Differential Amplifier

Thus far we have used only one of the operational amplifiers inputs to connect to the amplifier, using either the “inverting” or the “non-inverting” input terminal to amplify a single input signal with the other input being connected to ground. But we can also connect signals to both of the inputs at the same time producing another common type of operational amplifier circuit called aDifferential Amplifier.

By connecting each input in turn to 0v ground we can use superposition to solve for the output voltageVout. Then the transfer function for aDifferential Amplifiercircuit is given as:

When resistors,R1 = R2andR3 = R4the above transfer function for the differential amplifier can be simplified to the following expression:

Furthermore if R3=R1 then

This is the final expression of differential amplifier(difference amplifier) .

4.The Integrator Amplifier

Op-amp Integratoris an operational amplifier circuit that performs the mathematical operation ofIntegration, that is we can cause the output to respond to changes in the input voltage over time as the op-amp integrator produces anoutput voltage which is proportional to the integral of the input voltage. 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. The circuit diagram of the op-amp integrator cicuit is shown below:

When a step voltage,Vinis firstly applied to the input of an integrating amplifier, the uncharged capacitorChas very little resistance and acts a bit like a short circuit allowing maximum current to flow via the input resistor,Rinas potential difference exists between the two plates. No current flows into the amplifiers input and pointXis a virtual earth resulting in zero output. As the impedance of the capacitor at this point is very low, the gain ratio ofXc/Rinis also very small giving an overall voltage gain of less than one, ( voltage follower circuit ).As the feedback capacitor,C begins to charge up due to the influence of the input voltage, its impedanceXcslowly increase in proportion to its rate of charge. The capacitor charges up at a rate determined by the RC time constant, (τ) of the series RC network. Negative feedback forces the op-amp to produce an output voltage that maintains a virtual earth at the op-amp’s inverting input.

Since the capacitor is connected between the op-amp’s inverting input (which is at earth potential) and the op-amp’s output (which is negative), the potential voltage,Vcdeveloped across the capacitor slowly increases causing the charging current to decrease as the impedance of the capacitor increases. This results in the ratio ofXc/Rinincreasing producing a linearly increasing ramp output voltage that continues to increase until the capacitor is fully charged.At this point the capacitor acts as an open circuit, blocking any more 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).

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 thisRCtime constant value, either by changing the value of the Capacitor,Cor the Resistor,R, the time in which it takes the output voltage to reach saturation can also be changed for example.AsWe 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 givingQ/C. Then the voltage across the capacitor is outputVouttherefore:-Vout=Q/C. If the capacitor is charging and discharging, the rate of charge of voltage across the capacitor is given as:

ButdQ/dtis electric current and since the node voltage of the integrating op-amp at its inverting input terminal is zero,X = 0, the input currentI(in)flowing through the input resistor,Rinis given as:

The current flowing through the feedback capacitorCis 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 theOp-amp Integrator as:

Simplifying above equation as,

Whereω=2πƒand the output voltageVoutis a constant1/RCtimes the integral of the input voltage Vinwith respect to time. The minus sign (–) indicates a 180^ophase shift because the input signal is connected directly to the inverting input terminal of the op-amp.

5.The Summing Amplifier

The Summing Amplifier is a very flexible circuit based upon the standardInverting Operational Amplifierconfiguration. As its name suggests, the “summing amplifier” can be used for combining the voltage present on multiple inputs into a single output voltage. The ciruit diagram of summing amplifier is shown below:

The output voltage, (Vout) now becomes proportional to the sum of the input voltages,V1,V2,V3etc. Then we can modify the original equation for the inverting amplifier to take account of these new inputs thus:

However, if all the input impedances, (Rin) are equal in value, we can simplify the above equation to give an output voltage of:

We now have an operational amplifier circuit that will amplify each individual input voltage and produce an output voltage signal that is proportional to the algebraic “SUM” of the three individual input voltagesV₁,V₂andV₃. We can also add more inputs if required as each individual input “see’s” their respective resistance,Rinas the only input impedance.This is because the input signals are effectively isolated from each other by the “virtual earth” node at the inverting input of the op-amp. A direct voltage addition can also be obtained when all the resistances are of equal value andRƒis equal toRin.

AScaling Summing Amplifier can be made if the individual input resistors are “NOT” equal. Then the equation would have to be modified to:

Simplifying above equation as,

This allows the output voltage to be easily calculated if more input resistors are connected to the amplifiers inverting input terminal. The input impedance of each individual channel is the value of their respective input resistors, ie,R₁, R₂, R₃… etc.

Sometimes we need a summing circuit to just add together two or more voltage signals without any amplification. By putting all of the resistances of the circuit above to the same valueR, the op-amp will have a voltage gain of unity and an output voltage equal to the direct sum of all the input voltages as shown:

Attenuation:

Attenuation refers to a reduction in signal strength commonly occurring while transmitting analog or digital signals over long distances. It is the reverse process of signal amplification. The circuit which performs the reverse process of amplification is known as attenuator circuit. Causes of attenuation in both signal frequency and range between the end points of the medium, affect the amount of signal reduction. As the range increases, attenuation also increases. Attenuation is historically measured in dB but it can also be measured in terms of voltage.

Basically there are two types of attenuator circuits. They are:

1. Passive attenuator circuit
2. Active attenuator circuit

Passive attenuator circuit:

A Passive Attenuator is a special type of electrical or electronic bidirectional circuit made up of entirely resistive elements. An attenuator is a two port resistive network designed to weaken or “attenuate” (hence their name) the power being supplied by a source to a level that is suitable for the connected load.

Apassive attenuatorreduces the amount of power being delivered to the connected load by either a single fixed amount, a variable amount or in a series of known switchable steps. Attenuators are generally used in radio, communication and transmission line applications to weaken a stronger signal.

ThePassive Attenuatoris a purely passive resistive network (hence no supply) which is used in a wide variety of electronic equipment for extending the dynamic range of measuring equipment by adjusting signal levels, to provide impedance matching of oscillators or amplifiers to reduce the effects of improper input/output terminations, or to simply provide isolation between different circuit stages depending upon their application as shown above.Simple attenuator networks (also known as “pads”) can be designed to produce a fixed degree of “attenuation” or to give a variable amount of attenuation in pre-determined steps. Standard fixed attenuator networks generally known as an “attenuator pad” are available in specific values from 0 dB to more than 100 dB. Variable and switched attenuators are basically adjustable resistor networks that show a calibrated increase in attenuation for each switched step, for example steps of -2dB or -6dB per switch position.Then anAttenuatoris a four terminal (two port) passive resistive network (active types are also available which use transistors and integrated circuits) designed to produce “distortionless” attenuation of the output electrical signal at all frequencies by an equal amount with no phase shift unlike a passive type RC filter network, and therefore to achieve this attenuators should be made up of pure non-inductive and not wirewound resistances, since reactive elements will give frequency discrimination.

Wave Shaping.

Electronic circuits used to create or modify specified time varying electrical voltage or current waveform using combinations of active electronics devices ,such as transistors or analog or digital integrated circuits and resistors, capacitors and inductors is known as Wave shaping. Most wave shaping circuits are used to generate periodic waveforms such as square wave,sine and rectified sine waves, triangular waves etc.A number of traditional and electromechanical circuits are used to generate these waveforms .Sine wave generators and LC, RC and beat frequency oscillators are used to generate sine waves ; rectifiers , consisting of diode combinations interposed between sine wave sources and resistive loads,produce rectified sine waves.

Wave shaping may be Linear and Non-Linear.

Linear wave shaping involves passage of signal through linear systems such as Resistors, capacitors, and inductors and they do not change the waveform of the sinewave when it is transmitted through them.Example of Linear wave shaping circuits are RC-integrator, RC-differentiator etc.

Non-Linear wave shaping involves passage of signal through nonlinear systems such as diode, transistor etc and they alters the waveform of the sinewave when it is transmitted through them.Example of Non-Linear wave shaping circuits are Series diode clipper, Shunt diode clipper etc.

References-

1.S.morris.alan(2001). Measurement and Instrument principle(3 ed.).A division of Reed Educational and Professional Publishing Ltd

2.Robert Boylestad and Louis Nashelsky (1996). Electronics devisces and circuit theory(7 ed). Prentice Hall College Division.

3.Hayt, William; Kemmerly, Jack E. (1971), Engineering Circuit Analysis (2nd ed.), McGraw-Hill

4. Oppenheim, Alan V. Schafer, Ronald W. (1975). Digital Signal Processing. prentice hall