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AM 5-212

BASIC ELECTRONICS

OPERATIONAL AMPLIFIERS

MARCH 2012

DISTRIBUTION RESTRICTION: Approved for public release. Distribution is unlimited.

DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM

FORT HUACHUCA ARIZONA 85613-7070

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AM 5 – 212 – Operational Amplifier Design

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AM 5 – 212, Operational Amplifier Design

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Contents 1 INTRODUCTION....................................................................................................................... 1-1

1.1 General;............................................................................................................................ 1-1 1.2 Amplifier Open Loop Gain................................................................................................. 1-2 1.3 Op-amp slew rate.............................................................................................................. 1-2 1.4 Offset null ......................................................................................................................... 1-2 1.5 Operational amplifier packages......................................................................................... 1-1

2 OPERATIONAL AMPLIFIERS................................................................................................... 2-1 2.1 Introduction: ...................................................................................................................... 2-1 2.2 Basic inverting circuit: ....................................................................................................... 2-1 2.3 Op-amp variable gain amplifier circuit ............................................................................... 2-2

2.3.1 Introduction: .................................................................................................................. 2-2 3 OP AMPS AS A FILTERS ......................................................................................................... 3-3

3.1 Introduction: ...................................................................................................................... 3-3 3.2 Active Filter Types ............................................................................................................ 3-3

3.2.1 Low-Pass Filter: ............................................................................................................ 3-3 3.2.2 Bandpass Filter ............................................................................................................. 3-6 3.2.3 Band-Reject Filter ......................................................................................................... 3-6

3.3 FILTER RESPONSE......................................................................................................... 3-8 3.3.1 Butterworth ................................................................................................................... 3-8 3.3.2 Chebyshev.................................................................................................................... 3-9 3.3.3 Bessel ........................................................................................................................... 3-9

3.4 Bandpass Filter............................................................................................................... 3-10 3.4.1 Introduction: ................................................................................................................ 3-10 3.4.2 Forth Order (n=4) Low Pass Chebyshev Filter: ........................................................... 3-11

3.5 Notch Filter ..................................................................................................................... 3-13 4 OP AMP OSCILLATORS ........................................................................................................ 4-15

4.1 Introduction..................................................................................................................... 4-15 4.2 Crystal Oscillator Using a Comparator ............................................................................ 4-15 4.3 Square Wave Gernerator Circuit ..................................................................................... 4-16 4.4 Bistable multivibrator....................................................................................................... 4-17


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REFERENCES: Allied Communications Publications (ACP):

ACP - 121 - Communications Instruction, General ACP - 124 - Radiotelegraph Procedures ACP - 125 - Radiotelephone Procedures ACP - 126 - Communications Instructions – Radio Teletypewriter ACP - 131 - Communications Instructions Operating Signals

US Army Documents US Army Regulations

1. AR 25-6 - Military Auxiliary Radio System (MARS) and Amateur Radio Program

US Army FM/TM Manuals and Handbooks 1. FM 6-02.52 – Tactical Radio Operations 2. TM 5-811-3 - Electrical Design, Lightning and Static Electricity Protection 3. TM 5-682 - Facilities Engineering Electrical Facilities Safety 4. TM 5-690 - Grounding and Bonding in Command, Control, Communications,

Computer, Intelligence, Surveillance, and Reconnaissance (C4ISR) Facilities 5. TM 11-661 Electrical Fundamentals, Direct Current 6. TM-664 – Basic Theory and Use of Electronic Test Equipment

US Army Handbooks 1. MIL-HDBK 1857 - Grounding, Bonding and Shielding Design Practices

US Army MARS Documents

1. US Army MARS Net Plan

Commercial References 1. Basic Electronics, Components, Devices and Circuits; ISBN 0-02-81860-X, By William

P Hand and Gerald Williams Glencoe/McGraw Hill Publishing Co. 2. Standard Handbook for Electrical Engineers - McGraw Hill Publishing Co.


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1 INTRODUCTION

1.1 GENERAL;

Operational amplifiers, or Op-Amps, are one of the mainstays of the analog electronics. are versatile amplifiers. They provide a combination of parameters that are of great use:

o High gain o High input impedance o Low output impedance o Differential comparator

When used in the differential mode the two inputs enable it to be used to measure the difference between the levels applied to the two inputs. This level difference can be used in many ways which you will see later. The basic circuit symbol for an operational amplifier is a triangle as shown in Figure 1-1. The two

inputs are designated by "+" and "-" symbols, and the output of the operational amplifier is at the

opposite end of the triangle. Inputs from the "+" input appear at the output in the same phase, whereas signals present at the "-" input appear at the output inverted or 180 degrees out of phase.

The "+" input is obliviously the non-inverting input, while the "-" input is the inverting input of the

amplifier. This feature of the amplifier, which is difference in voltage between the two inputs, is why it is known as a differential amplifier.

Figure 1-1,

Operational Amplifier Symbol Generally the power supply is not shown in circuit diagrams and grounds are shown with the ground symbol. This like the digital logic diagrams, the power source and grounds for op amps are assumed to be there. The average op-amp utilizes two voltages +15 and -15 VDC, although this will change depending on the application and the actual chip used. The normal open circuit gain of the operational amplifier is very high. Typically in excess of 20,000 which is much to high to be stable without extra circuits. These extra circuits control feedback to the input thus establishing the major feature of the amplifier, the feedback circuit..


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1.2 AMPLIFIER OPEN LOOP GAIN

Since the gain is exceedingly high, feedback is applied back to the input of the amp so that the gain of the overall circuit is established by the feedback circuit. Open loop gain of an operational amplifier falls very rapidly with increasing frequency. Typically an op-amp has an open loop gain of more than 50,000, but normally will fall very rapidly. As an example the 741 IC Op-Amp begins to fall off at about 10 to 12 HZ.

1.3 OP-AMP SLEW RATE

With very high gains the operational amplifiers have what is termed compensation capacitance to prevent oscillation. This capacitance combined with the limited drive currents mean that the output of the amplifier is only able to change at a limited rate, even when a large or rapid change occurs at the input. This maximum speed is known as the slew rate. A typical general purpose device may have a slew rate of 10 V / microsecond. This means that when a large step change is placed on the input, the device would be able to provide an output 10 volt change in one microsecond. The figures for slew rate change are dependent upon the type of operational amplifier being used. Low power op-amps may only have a slew rate of a volt per microsecond, whereas there are fast operational amplifiers capable to providing slew rates of 1000 V / microsecond. The slew rate can introduce distortion onto a signal by limiting the frequency of a large signal that can be accommodated. It is possible to find the maximum frequency or voltage that can be accommodated. A sine wave with a frequency of f Hertz and amplitude V volts requires an operational amplifier with a slew rate of 2 x π x V x V volts per second.

1.4 OFFSET NULL

One of the minor problems with an operational amplifier is that they have a small offset. Normally this is small, but it is quoted in the datasheets for the particular operational amplifier in question. It is possible to null this using an external potentiometer connected to the three offset null pins. In most applications no provision is made for the offset null. This is because it is normally not a problem and it adds further components and an adjustment. However it can be a problem where large levels of DC gain are required. Here the offset voltage is amplified by the gain and could appear as a significant voltage at the output.


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1.5 OPERATIONAL AMPLIFIER PACKAGES

The packages in which electronics components are available is very important. Many electronics components are available in a wide variety of package styles, and the operational amplifier is not exception. Like many other electronics components, a vast number are used as surface mount components in mass produced electronics products. They are available in the SOIC (small outline integrated circuit) package as well as many others. Some are even available in five leaded versions of transistor packages and this makes them ideal to drop into a circuit without using up much board space. However the more traditional style of electronics component packages is also available. They are available in the DIL (dual in line) package, often as a single operational amplifier in an eight pin DIL, or duals in eight pin packages (with no offset null connections) or fourteen or sixteen pin DILs. Operational amplifiers are in widespread use in analogue electronics design and production. These op amps provide a particularly useful combination of circuit parameters that make them an indispensable tool for the electronics design engineer. While digital electronics is growing, the use of op-amps will nevertheless remain in vast quantities as a result of their cost, performance and ease of use. These electronics components will therefore remain very cheap for many years to come.


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2 OPERATIONAL AMPLIFIERS

2.1 INTRODUCTION:

Operational amplifiers can be used in a wide variety of circuit configurations. One of the most widely used is the inverting amplifier configuration. It offers many advantages from being very simple to use, requiring just the operational amplifier integrated circuit and a few other components. Circuits are available for an inverting amplifier, and a non-inverting amplifier.

2.2 BASIC INVERTING CIRCUIT:

The basic circuit for the inverting operational amplifier circuit is shown below. It consists of a resistor from the input terminal to the inverting input of the circuit, and another resistor connected from the output to the inverting input of the op-amp. The non inverting input is connected to ground.

Figure 2-1

Basic Inverting Operational Amplifier Circuit

In this circuit the non inverting input of the operational amplifier is connected to ground. As the gain of the operational amplifier itself is very high and the output from the amplifier is a matter of a few volts, this means that the difference between the two input terminals is exceedingly small and can be ignored. As the non-inverting input of the operational amplifier is held at ground potential this means that the inverting input must be virtually at earth potential (i.e. a virtual earth). It is easy to derive the calculation for the op-amp gain. The input to the op-amp itself draws no current and this means that the current flowing in the resistors Rf and Rin is the same. Using ohms law

Vout Rf Voltage Gain = Vin

= Rin

As an example, an amplifier requiring a gain of ten could be built by making Rf 47 k ohms and Rin 4.7 k ohms.

NOTE For high levels of gain, the gain bandwidth product of the basic op amp itself may become a problem. With levels of gain of 100, bandwidth of some operational amplifier ICs may only be around 3 kHz. Check the data sheet for a given chip being used before settling on gain.


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2.3 OP-AMP VARIABLE GAIN AMPLIFIER CIRCUIT

2.3.1 Introduction:

Most operational amplifier circuits have a fixed level of gain. However it is often useful to be able to vary the gain. This can be done simply by using a potentiometer on the output of a fixed gain op-amp, but sometimes it may be more useful to vary the actual gain of the amplifier circuit itself. This can be achieved very simply by using the variable gain operational amplifier circuit as shown in Figure 2-4. The circuit is very simple, and only uses one additional component over that of a basic operational amplifier circuit. The circuit simply uses a single variable gain amplifier. The circuit uses a single operational amplifier, two resistors and a variable resistor. Additionally not only is the gain varied but also the sign.

Figure 2-4

Variable Gain Circuit


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3 OP AMPS AS A FILTERS

3.1 INTRODUCTION:

Operational amplifiers make good active filter circuits, including a high pass, low pass or band pass (narrow band) filter circuit. Using a few components they are able to provide high levels of performance. The simplest high pass filter circuit is a capacitor in series with one of the resistors. The capacitor reactance increases as frequency falls, and as a result this forms a CR low pass filter providing a roll off of 6 dB per octave. The cut off frequency or break point of the filter can be calculated by using the formula:

1 Xc =

2 πFC where:

Xc = capacitive reactance in ohms π = Greek letter and equal to 3.14159 f = frequency in Hertz C = capacitance in Farads

3.2 ACTIVE FILTER TYPES

3.2.1 Low-Pass Filter:

A low-pass filter will selectively differentiate frequency domain signals based on a designer-assigned break frequency. Signals below the break frequency are passed through the filter with little or no attenuation. Any signal above the break frequency is rejected or nulled. Reference Figure 3-1.

Figure 3-1

Typical Low Pass Filter Response The passband of a low-pass filter extends from near zero to the break frequency. The break frequency, f1, occurs at the frequency where amplitude has decreased to 0.707 times its value near zero hertz. This is commonly referred to as the filter 3 dB frequency. Passband is then equal to the 3 dB bandwidth. Amplitude response below 3 dB frequency is of primary importance in a lowpass filter.


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The slope of response between f1 and f2, where f2 = 2f1, determines the order of the filter response. This slope of filter response is usually expressed in dB/octave:

dB (AI - A2)dB

(log f2 - log fl) octave

= log 2

Another way of expressing the slope is in dB/decade, where a decade is 10 times f1 that is,f2 = 10f1 Slope may, therefore, be expressed in either dB/octave or dB/decade. For example, 6 dB/octave is equal to 20 dB/decade. Some filters, such as the Butterworth exhibit characteristics similar to the following:

Response dB/octave dB/decade Order n 6 20 1 12 40 2 18 60 3

Figure 3-2

Typical First-Order, Low-Pass Filter Combinations of active filter stages are used to obtain higher-order filters where n = 3, 4, 5, and so on.

3.2.1.1 First-order filter stage:

This filter is used to obtain an odd-order filter such as n = 1,3,5, and so on. In effect, a single-RC network is oriented around an op amp. Figure 32 shows an example of a typical first-order stage for low-pass operation. Gain in the passband is adjusted by changing the ratio Rtf R1; that in the stop band by R2/R1 for R2 < < Rf.

3.2.1.2 High-Pass Filter:

The high-pass filter is the mirror image of the low-pass filter. Signals below the 3 dB frequency are attenuated and those above are passed (Figure. 3-3). The passband of the ideal active high-pass filter extends to infinity. Operational amplifiers, however, have upper-frequency limits and the op amp therefore restricts the high-frequency response.


Ver. 1.0 3-5

Figure 3.3

Typical High-Pass Filter Response

3.2.1.3 High-Pass Filter With Gain:

Active filters have gain in the passband (Fig. 3.4). Thus, desired output levels must be considered in the design procedure.

Figure 3.4

Gain of a Filter in its Passband Active filter gains can be measured in decibels milliwatt (dBm), decibels relative to a power level of 1 mW into a 600 Ω load or decibels volts (dBV), and 1 Vrms into a 600 Ω load. It is necessary to consider signal levels when using active filters to stay within the dynamic range of the op amp. For example, if an active filter has a gain of 10 in the passband, a 1 V p-p input signal produces a 10 V p-p output. The amplifier must be capable of 10 V p-p operation at the cutoff frequency or distortion will occur.


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3.2.2 Bandpass Filter

When a pair of filters, one low pass and one high pass, are placed in series, the break frequency of a

low-pass filter is at fCL and the high-pass filter is at fCHH' The bandpass of the filter is equal to fCL- fCH

.(Reference Figure 3-5) and, fCH < fCL in the circuit. Bandpass active filters are easily made by using

dual or quad op amp packages.

Figure 3-5 Bandpass Filter Using Cascading Low and High-Pass Filter Stages

The higher the order of filter, the sharper the rolloff of bandpass response making amplitude reduction versus frequency occurs more rapidly as the order, n, increases. A measure of effectiveness of a bandpass filter in terms of rolloff is circuit Q. It is expressed by:

fo Q = ∆f

where fo is the center frequency of the filter and ∆f is the 3 dB bandwidth.

3.2.3 Band-Reject Filter

Figure 3.6, is a band-reject (band-stop) filter. This is the inverse of a bandpass filter. It can be derived from low-pass and high-pass filter sections in parallel. The passband of each filter section do not overlap except in the reject region. In this case, the breakpoint of the low-pass filter is below that of the high-pass filter such that

fCL < fCH'

A band-reject filter's effectiveness is judged by the depth of the notch and is measured by the ratio of the passband signal to the minimum signal in the stop-band, or notch, in decibels. Typically, attenuation in the stop band is greater than 50 dB.


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Figure 3.6 Band-Reject (Band-Stop) Filter


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3.3 FILTER RESPONSE

3.3.1 Butterworth

The Butterworth is one of the most popular filter types having good amplitude characteristics near zero frequency. The sharpness of the transition frequency increases with the order of the filter, as illustrated in Figure 3.7. Also, the phase response is more linear with frequency than other similar type filters.

(a) Amplitude Response

(b) Phase Response

Figure 3-7

Characteristics of a Butterworth Filter for Different Orders, n


Ver. 1.0 3-9

3.3.2 Chebyshev

This type filter is capable of a much sharper rolloff rate at the break frequency than is the Butterworth. Higher-order Chebyshev filters are, therefore, able to differentiate more efficiently between frequencies at the edge of the passband and those in the stop band. One major difference between the Butterworth and a same order Chebyshev is that the amplitude response of the latter has ripple in its passband (reference Figure 3.8). The ripple width may be controlled by the selection of filter parameters. The phase response of the Chebyshev filter is less linear than that of the Butterworth filter.

Figure 3-8 Response of a Chebyshev Filter

3.3.3 Bessel

The Bessel filter is also known as a constant time delay filter. The significance of constant time delay is particularly useful in circuits for processing variable frequency signals, such as tone bursts, pulse trains, and other unique systems of information transfer.


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3.4 BANDPASS FILTER

3.4.1 Introduction:

The simplest bandpass filter is a capacitor across the feedback resistor. As the frequency rises there is an increasing the level of feedback as the reactive impedance of the capacitor falls. The break point is the frequency at which the reactance of the capacitor equals the resistance of the resistor. This can be achieved using the diagram and formulas:

Figure 3-9

Typical Bandpass While these operational amplifier circuits are useful to provide a reduction in gain at high frequencies, they only provide an ultimate rate of roll off of 6 dB per octave, i.e. the output voltage halves for every doubling in frequency. This type of filter is known as a one pole filter. Often a much grater rate of rejection is required, and to achieve this it is possible to incorporate a higher performance filter into the feedback circuitry and multiple stages.


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3.4.2 Forth Order (n=4) Low Pass Chebyshev Filter:

Although it is possible to design a wide variety of filters with different levels of gain and different roll off patterns using operational amplifiers, the filter shown in Figure 3-10 will give a good performance. I have used this design in several situations that required a definite roll off in response and it worked beautifully.

Figure 3-10 4th Order Low Pass Chebyshev Filter

3.4.2.1 Design Example:

The requirement was for a low-pass filter with a break point at 10 KHz but with a unity gain. This design uses a Voltage Controlled Voltage Source and has a fast roll-off, a forth order Chebyshev response. The NE5532 dual op amp was selected. This chip is internally compensated at unity gain

The calculations for the circuit values are very straightforward and will be given step by step.

1 Multiplier constant, K is needed. The expression for K is:

K = 100/(feC')

where fe is the cutoff frequency and C' is in microfarad (ILF). 3 Select C = O.O1ILF. Substitution of values in the equation yields:

K = 100/(104 X 0.01) = 1

2 A 0.5 dB ripple in the passband is acceptable. Referring to Table 3.1, we obtain:


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Table 3.1 Fourth-order low-pass Chebyshev cascaded VCVS filter design (0.5 dB)*

Circuit Element Values

Gain 1 2 6 10 36 100 Stage

Rl 7.220 4.538 1.303 0.808 0.808 0.547

R2 12.219 0.525 1.828 2.948 1.474 2.177 R3 Open 10.126 4.696 4.695 2.738 3.027 1 R4 0 10.126 9.393 18.781 13.692 27.240

C1 0.027C C C C 2C 2C

Rl 2.994 2.994 1.880 1.880 1.033 0.773

R2 5.050 0.050 3.781 3.781 3.440 4.596 R3 Open Open 11.321 11.321 5.368 5.966 2 R4 0 0 11.321 11.321 26.838 53.695

C1 0.47C 0.47C C C 2C 2C

a Resistances in kilohms for a K parameter of 1.

Stage 1

R1= 7.220 x 1 = 7.22 k R2 = 12.219 x 1 = 12.219 k R3 = Open R4 = 0 C1 = 0.027 x 0.01 J.1F = 270 pF Use 7.5 k 12 k 270 pF

Stage 2

R; = 2.994 x 1 = 2.994 k R_ = 5.050 x 1 = 5.05 k R_ = open


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3.5 NOTCH FILTER

Operational amplifiers can be used to make notch filter circuits like that shown in Figure 3-11 A notch filter is used to remove a particular frequency, having a notch where signals are rejected. Often they are fixed frequency, but some are able to tune the notch frequency. Having a fixed frequency, this operational amplifier, op amp, notch filter circuit may find applications such as removing fixed frequency interference like mains hum, from audio circuits. The diagram below shows a notch filter circuit using a single op amp. The notch filter circuit is quite straightforward and the calculations for the component values are also easy.

Figure 3-11

Active Notch Filter Circuit

A Notch Filter employs both negative and positive feedback around the operational amplifier chip and is thus able to provide a high degree of performance. Calculation of values for the circuit is very straightforward. The equation for resistor and capacitor values for the notch filter circuit is:

1 Fnotch =

(2πRC) Where:

Fnotch = centre frequency of the notch in Hertz π = 3.142 R and C are the values of the resistors and capacitors in Ohms and Farads

To build this circuit, high tolerance components must be used to obtain best performance. They need to be 1% or better. A notch depth of 45 dB can be obtained using 1% components, although in theory it is possible for the notch to be of the order of 60 dB using ideal components. R1 and R2 should be matched to within 0.5% or they may be trimmed using parallel resistors. A further item for optimum performance is to ensure that the source impedance is less than about 100 ohms. Additionally the load impedance should be greater than about 2 M Ohms. Typical values for a 50 Hz notch are:

C1, C2 = 47 nfd R1, R2 = 10 k, R3, R4 = 68 k.


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4 OP AMP OSCILLATORS

4.1 INTRODUCTION

Oscillators are used in many electronics circuits and they are simple to construct. It is possible to construct them using a couple of transistors, but it is also possible to construct a very simple oscillator circuit using the operational amplifier. The circuit can be used in a variety of applications where a simple square wave oscillator circuit is required. The use of an operational amplifier integrated circuit is ideal from many viewpoints. Although circuits can be made using just two transistors, operational amplifiers are also very cheap these days, and there is often little to choose in terms of cost.

4.2 CRYSTAL OSCILLATOR USING A COMPARATOR

Another useful and inexpensive crystal oscillator can be designed around an analog comparator Ie. One possible advantage of this circuit over the CMOS crystal oscillator is the possibility of extending the upper frequency limits and the availability of more current drive. In Fig. 4-1, resistors R3 and R4 are equal so that the comparator switches symmetrically about ( + V)/2 V. The specific time constant R2C is non-critical and is determined primarily by the availability of component values. If the time constant R2C is greater than 3/f, where f is the frequency of oscillation, then a 50% duty cycle is obtained by maintaining a dc voltage at the inverting input equal to the absolute average value of the output waveform.

Resistor R1, a pull-up resistor, is optional. For a 50% duty cycle,

Figure 4-1


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Simple Crystal Oscillator

4.3 SQUARE WAVE GERNERATOR CIRCUIT

The operational amplifier square wave generator circuit, as shown in Figure 4-2 utilizes an RC feedback network to the inverting input and resistive feedback to the non-inverting input of an op amp. The ratio of Rl to the sum of Rl and Rz defines the threshold for switching. When the output is at + V, timing capacitor C charges from negative threshold to positive threshold. When the positive threshold is reached, output switches to - V and capacitor begins charging from the positive threshold back to negative threshold.

Figure 4-2 Operational Amplifier Multivibrator Oscillator

If R1 + 0.86 R2 then the oscillation frequency f will be:

1

f = 2RC

If R does not equal R2, then the oscillation frequency will be:

1 f =

2RC in (2R2 / R2 +1


Ver. 1.0 4-17

4.4 BISTABLE MULTIVIBRATOR

It is easy to use an operational amplifier as a bistable multivibrator is shown in Figure 4-3. An incoming waveform is converted into short pulses and these are used to trigger the operational amplifier to change between its two saturation states. To prevent small levels of noise triggering the circuit, hysteresis is introduced into the circuit, the level being dependent upon the application required. The operational amplifier bistable multivibrator uses just five components, the operational amplifier, a capacitor and three resistors.

Figure 4-3 Bistable Multivibrator Circuit

The bistable circuit has two stable states. Figure 4-4 show the positive and negative saturation voltages of the operational amplifier operating with the given supply voltages. The circuit can then be switched between them by applying pulses. A negative going pulse will switch the circuit into the positive saturation voltage, and a positive going pulse will switch it into the negative state.

Figure 4-4 Waveforms for the Bistable Multivibrator Circuit

It is very easy to calculate the points at which the circuit will trigger. The positive going pulses need to be greater than Vo-Sat through the potential divider.

R3 V o-Sat x R2 + R3

and similarly the negative going pulses will need to be greater than Vo Sat through the potential divider, i.e. VoSat x R3 / (R2 + R3). If they are not sufficiently large then the bistable will not change state.