Electronic Analog Computer

Dr. Amin Danial Asham

by

What is Computer:A computer is a machine which performs mathematical computations.

In general, computers may be classified as:

A.Analog ComputersB. Digital Computers

An analog computer is a form of computer that uses the continuously changeable aspects of physical quantities such as electrical, mechanical, or hydraulic quantities to model the problem being solved.

In this sort of computer, numbers are represented by continuously-varying quantities.

Since electronic analog computers can be easily constructed and adjusted, they are used to simulate mechanical systems and get all measurements directly with an oscilloscope.

A. Analog Computers

A. Analog ComputersHeathkit EC-1 educational analog computer

http://en.wikipedia.org/wiki/Analog_computer

A. Analog ComputersPolish analog computer ELWAT

http://en.wikipedia.org/wiki/ELWAT

A. Analog Computers

Polish analog computer AKAT-1

http://en.wikipedia.org/wiki/Analog_computer

Physical quantities such as weight, temperature or area are represented by voltages. Voltage is the electrical analog of the variable being analyzed. Arbitrary scale factors are set up to relate the voltages in the computer to the variables in the problem being solved.

For example, 1 volt equals 5 meters or 10 volts equals 1 kg. The name "analog" comes from the fact that the computer solves by analogy by using physical quantities to represent numbers.

A. Analog Computers (continue)

B. Digital Computers:

Operate by discrete steps, that is, they actually count. Numbers are represented by sets of 1's and 0's where

1 and 0 are represented by two different voltages. Operations are simple logical operations (i.e. AND, OR,

etc.) or arithmetic operations (i.e. addition or subtraction) . Calculus-type (differentiation and integration) operations are very complicated to do.

Common Examples of Calculator, Programmable Logic Controller, Personal Computers, Tablets,……etc

Analog computers are especially useful in solving dynamic problems in which the motion can be expressed in the form of a differential equation.

This type of computers can perform addition, multiplication by a constant, integration, and differentiation based on the used elements and the configuration of the circuit.

Since the analog computer can perform these operations, thus it is a convenient device for the solution of differential equations.

The fundamental building block of the electronic analogue computer is the Operational Amplifier.

A. Electronic Analog Computers

I. Operational Amplifier (Op-Amp IC)

Op-Amp is a differential DC coupled voltage Amplifier.

Where • is the output.• is the non inverting input.• is the inverting input.• is the positive power supply.• is the negative power supply.

I. Operational Amplifier (Op-Amp) (continue) An equivalent circuit of an operational amplifier.

Where

• is the open loop gain.• input impedance.• output impedance.

𝑮𝑶𝑳𝑽 𝒊𝒏

𝑽 𝒊𝒏=𝑽 +¿−𝑽 −¿

𝑉 +¿ ¿

𝑉 −

𝑉 𝑜𝑢𝑡

𝒁 𝒐𝒖𝒕𝒁 𝒊𝒏

I. Operational Amplifier (Op-Amp) (continue)Typical Op-Amp

• has a typical value g.•is very high impedance which is of order M ohms. •is low impedance which is typically around 50 ohms.

Properties of Op-Amp• and are considered zero because of the high input impedance. •The open loop gain:

Vin

LM324

𝐼 +¿¿

𝐼−

𝑉 𝑠+¿ ¿

𝑉 𝑠−

Because of very high open loop gain we get a Narrow

Linear Region.

Saturation regions where is limited by characteristics of the internal circuit and the power supply

I. Operational Amplifier (Op-Amp) (continue)

The relation between the and

I. Operational Amplifier (Op-Amp) (continue) Because the is very large it is considered infinity. Since the output voltage

• Therefore, as we get .• However, is limited by the internal circuit characteristics of the OpAmp and the

power supply.In Saturation region the relation between and is non-linear.The linear region as shown in the Input-Output curve is very narrow and corresponds to very small values of.In the Linear region:

Since

Therefore,

as is limited and , therefore

Therefore

II. Basic Mathematical Operations To use the Op-Amp as an amplifier in the linear region a negative

feedback is used to keep close to zero and hence getting in the linear region. Mathematical operations are implemented with amplifiers such as:

Multiplication by constant

Addition or Summation

Subtraction

Integration

Differentiation

An open loop Op-Amp circuit is used as a comparator. In this application the output is either high saturated or low saturated in response to the difference between and . Therefore, the Op-Amp produces 1 or 0 as a result of comparing two signals where 1 is high saturated value and 0 is low saturated value or vice versa.

II. Basic Mathematical Operations (continue)

Note: For simplicity the power supply terminals will be omitted.

Basic Rules for Closed Loop Op-Amp Circuits as Amplifiers:

a) because of

b) and because of the high input impedance.

c) Output Impedance is small compared to the input impedance of load

and hence negligible.

V +¿ ¿

V −

I +¿ ¿

I−

Inverting Amplifier

𝑉 𝑖 𝑉 𝑜

I

II. Basic Mathematical Operations (continue) a) Multiplications by Constant This operation can be implemented by inverting and non-inverting amplifiers.

i. Inverting Amplifier From the circuit diagram and applying the basic rules we get the

following relations:• Since , therefore the same current is passing through and • Since , we get that , hence

=

I

𝑽 −=𝟎

𝑺𝒂𝒎𝒆𝒄𝒖𝒓𝒓𝒆𝒏𝒕

II. Basic Mathematical Operations (continue)

a) Multiplication by constant (continue)

i. Inverting Amplifier (continue)

• The gain of the inverting amplifier is • The input voltage is multiplied by • The input impedance of the amplifier is

•Example Design an inverting amplifier of gain -4

•Solution Since

Therefore,

If we choose Therefore, Inverting Amplifier

𝑉 𝑖 𝑉 𝑜

II

II. Basic Mathematical Operations (continue) a) Multiplication by constant (continue)

ii. Non-Inverting Amplifier

Using the basic rules we get:• From the first rule we get

• From the second rule, the same current is passing through and

Notes:

𝑉 𝑖 𝑉 𝑜

𝑽 𝒊

𝑰

𝑰

Non-Inverting Amplifier

• The effective input resistance of the non-inverting circuit is at least as high as that of the operational amplifier itself.

• The Gain = is positive and higher than one.

•Example Design an non-inverting amplifier of gain 3

•Solution Since

Therefore,

If we choose 𝑉 𝑖 𝑉 𝑜

Non-Inverting Amplifier

II. Basic Mathematical Operations (continue) a) Multiplication by constant (continue)

ii. Non-Inverting Amplifier (continue)

Voltage Follower Amplifier

𝑉 𝑖𝑉 𝑜

• The effective input resistance of the non-inverting circuit is at least as high as that of the operational amplifier itself.

• The gain is Unity.

• This amplifier can be derived from Non-inverting amplifier by putting or i.e. removed.

• As a special case of non-inverting amplifier is voltage follower amplifier.

II. Basic Mathematical Operations (continue) a) Multiplication by constant (continue)

Sometimes it is needed to multiply by a fractional constant, which can be obtained by using an inverting amplifier with gain less than unity , i.e. . However, amplifiers with gain less than unity may cause unstable operation. Therefore this

method is undesirable. It is more desirable to use a potential

divider as shown, where 𝑅𝑖

𝑅𝑜

𝑉 𝑖

𝑉 𝑜

Thanks