A Manual explaining the basic Components, Devices and

Experimental Methods employed in an Electronic

Instrumentation Lab for Scientists.

MULTIMETER.

Digital Multi Meters (or DMMs abbreviated) and Digital Volt Meters (or DVMs

abbreviated) have replaced analog meters foe measuring voltages, currents and

resistances. The multi meters we are using have various input jacks that accept banana

plugs and one can connect the meter to the circuit under test using two banana plug leads.

Depending on how we configure the meter and its leads we can measure:

The voltage difference between the two leads.

The current flowing through the meter from one lead to the other

The resistance connected between its leads.

Multi meters usually have a selector knob, which allows us to select what is to be

measured and to set the full scale range of the display to handle inputs of various size.

To avoid damaging the circuit before you power up the circuit under test, set the meter at

its highest scale to avoid overflowing it.

THE BREADBOARD.

Breadboards are tools that help us build and test electric circuits. They include not only

sockets for plugging in components and connecting them together, power supplies, a

function generator, switches, logic displays etc.

Illustration showing many of the basic features of a breadboard with internal

connections shown for clarity. Note that each vertical column is broken into halves

with no built in connection between the top and the bottom.

The breadboard sockets contain spring contacts. If a wire is pushed inside a socket the

contacts press against it making an electrical connection. The sockets are internally

connected in groups of five (horizontal rows) or groups of twenty five (vertical columns).

Each power supply connects to a banana jack and also to a row of sockets running along

the to edge of the unit. The three supplies +5Volts (red jack in some breadboards), +15

Volts (yellow jack in some breadboards) and –15 Volts (blue jack in some breadboards)

have a common ground connection (black jack). The +15V and –15V supplies are

actually adjustable using the knobs provided, from less than 5V to greater than 15V.

MEASURING VOLTAGE

Voltage is always measured with respect to something usually a local ground (the

breadboard ground).

When connecting things is always a good idea to use color coding to help keep track of

which lead is connected to what. Use a black banana lead to connect to the “common”

input of the meter to the “ground” jack of the breadboard. Use a red banana plug with the

“V” input of the meter. Since the DMM is battery powered it is said to “float” with

respect to ground. It is therefore possible to measure the voltage drop across any circuit

element by simply connecting the DMM directly across the element.

Measuring Voltage. (a) An arbitrary circuit diagram is shown as an illustration on how

to use a voltmeter. Note that the meter measures the voltage drop across both the

resistor and the capacitor. (they have identical voltage drops since they are connected

in parallel). (b) A drawing of the same circuit showing how the leads of the DMM

should be connected when measuring voltage. Notice how the meter is connected in

parallel with the resistor.

When you operate the multi-meter always start from the scale with the highest

maximum reading and then you proceed to a finer scale according to your readings.

You never start measuring current from the finest scale unless you want to burn its

fuse.

MEASURING ELECTRIC CURRENT.

Current is measured by connecting a current meter (an ammeter or a DMM in its current

mode) in series with the circuit element through which the current flows. Ohm’s law

relates the current I, voltage V and resistance R according to V = IR. (Notice that this is

not a universal law of electric conduction since not ever material exhibits the property of

linearity between the electric current passing through it and the voltage applied across it.

Materials with such a linear relationship are being used to fabricate “resistors”.

Measuring current. (a) Schematic diagram of a series circuit consisting of a power

supply a 10k potensiometer and a multimeter. (Notice that in this diagram the center

tap of the potensiometer is left unconnected. If we accidentally connect it to the power

supply or to the ground excessive current could flow and burn out the pot). (b) A

drawing of the same circuit showing how the DMM leads should be configured to

measure current. The meter is connected in series with the resistor.

In order to measure current it is necessary to break the circuit in order to connect the

ammeter in series to the element the current through which we want to measure. We also

need to ensure ourselves that indeed the same current we want to measure passes through

the ammeter as well.

This is demonstrated in the following examples. Notice the way the circuit has been

broken in order for the Ammeter to be inserted.

EXAMPLE 1:

In the above circuit the Ammeter measures the current supplied by the battery. It DOES

NOT measure the current through R1, R2 or R3 resistors, but the sum of these three

currents.

EXAMPLE 2:

In the circuit below the circuit has been broken in various parts and Ammeters have been

inserted. What current is each Ammeter measuring?

1) Ammeter A1 is measuring the (total) current supplied by the 12 Volt battery. You can

calculate this current by dividing the 12 Volts voltage by the net resistance seen by the

battery (R1 through R4 in parallel).

2) Ammeter A2 is measuring the current passing through the resistance R1.

3) Ammeter A4 is measuring the current passing through the resistance R2.

4) Ammeter A6 is measuring the current passing through the resistance R3.

8) Ammeter A7 is measuring the current passing through the resistance R4.

9) Ammeter A3 is measuring the current flowing from node X to node Y. This is the sum

of the currents flowing through resistances R2, R3 and R4. Therefore the reading of A3

should be equal to the sum of the readings of A4 plus A6 plus A7 or the sum of the

readings A4 plus A5.

10) Ammeter A5 is measuring the current flowing from node Y to node Z. This is the

sum of the currents flowing through resistances R3 and R4. Therefore the reading of A5

should be equal to the sum of the readings of A6 plus A7.

EXAMPLE 3:

In the figure above we can see the implementation of the electronic schematic on the left

with actual components and measuring devices on the right. Notice how the circuit is

broken and the Ammeter inserted in series with the resistor. The current flowing through

the Ammeter (and measured by it) is the same current flowing through the resistor.

Caution: You need to be CAREFULL when you measure ELECTRIC CURRENT.

There is a fuse inside the instrument to protect it from being destroyed. The fuse will

burn itself if the multi-meter draws more current than the maximum allowed. Since the

resistance of the multi-meter in Current measuring mode (ammeter) is very small, if

the current you try to measure is larger than the maximum reading of the scale the

fuse will burned and you will not be able to use it until we change it. When you operate

the instrument as an ammeter always start from the scale with the highest maximum

current reading and then you proceed to a finer scale according to your readings. You

never start measuring current from the finest current measuring scale unless you want

to burn its fuse.

THE EXPERIMENTS THAT YOU WILL DO ARE NOT

DESIGNED TO PROTECT YOUR INSTRUMENTS

FROM OVERLOADING. PLEASE READ CAREFULLY

THE NEXT STATEMENTS.

WHEN YOU MEASURE AN ELECTRIC CURRENT

BEFORE YOU TURN THE POWER ON ENSURE

YOURSELVES THAT:

1. THE MULTIMETER IS SET AT THE (AC OR DC)

CURRENT MEASURING MODE AND THAT IS AT

THE LARGEST CURRENT SCALE. IF YOU

OVERLOAD THE INSTRUMENT THE FUSE WILL

BURN ITSELF OFF SINCE THE INTERNAL

RESISTANCE OF THE IDEAL AMMETER IS 0.

2. YOU HAVE CONNECTED THE AMMETER IN

SERIES WITH THE ELEMENT THE CURRENT

THROUGH WHICH YOU WANT TO MEASUER. IF

THE CONNECTION IS ACCIDENTALLY IN

PARALLEL THE FUSE OF THE INSTRUMENT WILL

BURN ITSELF OFF SINCE YOU WILL SHORT THE

ELEMENT BECAUSE OF THE LOW INTERNAL

RESISTANCE OF THE AMMETER.

MEASURING RESISTANCE.

Resistances usually are little cylinders of carbon, carbon film, metal film or wound up

wire encased in an insulating coating with wire leads striking out the ends. Often the

resistance is indicated by means of color stripes according to the resistor color code.

Resistors come in various sizes according to their power rating. The common sizes are

1/8 W, ¼ W, ½ W, 1 W and 2 W.

The resistance in Ohms is the sum of the values in columns 1 and 2 multiplied by the

value in column 3 plus or minus the tolerance in column 4. For example the color code

for an 1kΩΩΩΩ resistor would be “brown-black-red”, for a 51ΩΩΩΩ “green-brown-black”, for a

330ΩΩΩΩ “orange-orange-brown”, etc.

A potentiometer is a special type of resistor that has an adjustable “center-tap” or

“slider”, allowing electrical connections to be made not only at the two “ends”, but also

at an adjustable point along the resistive material. The voltage of this adjustable point

depends on the setting of the potentiometer’s knob. Warning: If you accidentally connect

power or ground to the potentiometer’s center tap, you can easily burn it out rendering it

useless. If in doubt have someone check your circuit before turning on the power.

MEASURING CURRENT WITH A VOLTMETER.

We can use a Voltmeter to measure the current passing through a resistance. First,

measure the resistance and then measure the voltage drop across the resistance with the

voltmeter. Finally use Ohm’s law to find out the current. This technique is very useful

when the ammeter fuse is burned and we cannot measure (especially small) currents

directly. We can use this technique only with resistances not with dynamic elements like

diodes or transistors.

CAPACITOR VALUE CODING

For some type of capacitors their value (and units) appear explicitly written on their

bodies. Other types of capacitors have their value encoded using color code.

Certain types of small capacitors (polyester, ceramic or mylar) capacitors have their

value written on them. On their body their written value is encrypted in a three digit

number . The first two digits indicate the first two most significant digits of their

numerical value. The third digit indicates the number of zeros after the two most

significant digits. The numerical value that appears this way is in pico Farads.

Example: Suppose you see the number

324 printed on the body of the capacitor.

The numerical value of the Capacitance

indicated is:

320000 pF or 320 nF or 0.32 µF

Next to the numerical value of the

capacitor a letter is usually printed

indicating the tolerance of the capacitor. Here are some tolerances and the corresponding

letters

%80%20%,50%20%,0%100

%20%,10%,5,5.0,25.0

+−=+−=−+=

±=±=±=±=±=

ZYP

MKJpFDpFC

THE PROBE

Oscilloscopes come with probes. Probes are cables that have a coaxial connector on one

end for connecting to the oscilloscope and a special tip on the other for connecting to any

desired point of the circuit to be tested. Top increase the scope’s input impedance and

affect the voltage to be measured as little as possible we can use a “10X” attenuating

probe which has circuitry inside that divides the signal voltage by 10. Some oscilloscopes

sense the nature of the probe and automatically correct for this factor of 10; other

oscilloscopes need to be told by the user which attenuation setting is in use. Note that a

probe has an alligator clip that connects to the shield of the coaxial cable (ground) which

is useful in reducing noise when probing high frequency or low voltage signals. Since it

is connected directly to the scope’s case, which is grounded via the third prong of the AC

power plug, it must be never allowed to touch any point of a circuit other than the

ground. Otherwise you will create a short circuit, which could damage circuit

components. This is no problem if you are measuring a voltage with respect to ground.

But if you want to measure a voltage drop between two points in the circuit neither of

which is at ground, first observe one point then observe the other. The difference between

the two measurements is the voltage drop across the element. During this process the

alligator clip of the probe should always be attached firmly to ground.

An attenuating probe can distort a signal. The manufacturer therefore provides a

“compensation adjustment” screw, which needs to be tuned for minimum distortion

An oscilloscope should have built in a calibration circuit that outputs a standard square

wave you can use to test a probe. Display the calibration square wave signal on the scope.

If the signal looks distorted carefully adjust the probe compensation using a small

screwdriver.

THE OSCILLOSCOPE

Illustration of a typical digital oscilloscope. The basic features to be used are shown.

Note the location of the AUTOSET button. When everything else fails try “autoset”.

Vertical controls.

There is a set of vertical controls for each oscilloscope channel. These adjust the

sensitivity (Volts per vertical division on the screen) and offset (the vertical position of

the beam on the screen when the input voltage is 0). The “CH1” and “CH2” menu

buttons can be used to turn the display of each channel on and off. They also select,

which control settings are programmed by the push buttons to the right of the screen.

Horizontal sweep.

To the right of the vertical controls there are the horizontal controls. Normally the scope

displays voltage on the vertical axis and time on the horizontal. The SC/DIV knob sets

the sensitivity of the horizontal axis (time per horizontal division on the screen). The

POSITION knob moves the image horizontally on the screen.

Triggering.

Triggering is the most complicated function performed by the scope. To create a stable

image of a waveform the scope must “trigger” its display at a particular voltage known as

the trigger “threshold”. The display is synchronized whenever the input signal “crosses”

that voltage, so that many images of the signal occurring one after another can be

superimposed on the same place on the screen. The LEVEL knob sets the threshold

voltage for triggering. One can select whether triggering occurs when the threshold

voltage is crossed from below (rising edge triggering) or from above (“falling-edge”

triggering) using the trigger menu (or for some scope models using trigger control knobs

and switches). You can also select the signal source for the triggering circuitry to be

channel 1, channel 2, an external trigger signal or the 120 V AC power line.

Setting up the trigger can be tricky, that is why some oscilloscope models provide an

automatic set-up feature (via the AUTOSET button) which can lock in on any repetitive

signal presented at the input and adjust the voltage, the time sensitivities and the

triggering for a stable display.

GROUNDING.

We must be very careful when we ground various instruments. Although it is not very

clear when we look at the schematics, the output (or input) lead of the instrument labeled

as ground is also connected to the instrument case (chassis) as well as to the ground of

the power outlet. In the long run do not forget that there should be only one ground.

When we connect two instruments together we must ensure ourselves that the grounds

are also connected properly. Let us look at the following figure below.

A technician is attempting to display the voltage drop across the element labeled X at an

oscilloscope. He connects the ground of the probe to point B but since the grounds of the

two instruments are connected together (via the outlet ground), he essentially shorts

element Y (points B and G are forced to be at 0 Volts). The technician should find a

different way to display the voltage drop across element X.

TESTING DIODES.

Diodes exhibit low resistance and allow current to flow through them when forward

biased. When diodes are reverse biased they do not allow electric current to flow through

then and exhibit very high (practically infinite) resistance. In order to test a diode with a

multimeter we have to test it separately in the forward conducting and in the reverse

blocking mode.

In order to test the diode in the conducting forward mode with the multimeter we connect

the positive lead of the meter to the anode and the negative lead to the cathode of the

diode. For a normal Silicon diode the multimeter should display a low voltage of about

0.7 Volts, or a low resistance (between 1 and 30 Ohms).

To check the diode in the blocking mode connect the positive lead of the meter to the

cathode and the negative lead to the anode of the diode. The multimeter should display a

very high resistance (a thousand times the low resistance or an out of range reading).

Some multimeters have a special setting for diode testing. The experimental setup is

shown below.

TESTING TRANSISTORS.

Transistors can be considered as two back to back connected diodes. A PNP transistor is

two pn diodes with a common N layer (N base) and an NPN transistor two pn diodes with

a common P layer (P base). Both junctions should be tested separately in the forward

conducting and the reverse blocking mode for each type of transistor. The way of testing

is the same as described in the case of diodes.

The setup for testing is shown below for a pnp transistor. In the left part of the figure the

junctions are biased in the forward mode and they are registering very low resistance in

the multimeter. In the right part of the figure the junctions (Collector Base and Base

Emitter) are biased in the blocking mode and the multimeter is registering out of range

resistance.

Finally the biasing the Collector Emitter leads of the transistor should always register

very high resistance (non conducting mode since there is no voltage at the base).

VOLTAGE SOURCES.

A voltage source (supply) is a device that forces a fixed voltage difference between the

leads of a load independent on the resistance of the load

RL. The current supplied by the voltage source is

calculated with the aid of Ohm’s Law and the resistance

of the load.

A practical Voltage Source has a small output

resistance r and can be approximated with an ideal

voltage source in series with the small output resistance

r of the non ideal supply.

A good voltage power supply must have an output

resistance much smaller than the load resistance in

order for the voltage appearing across the load to be

independent of the load itself.

Also a load that accepts an input signal in voltage form

must have a resistance much larger than the output

resistance of the signal source (voltage source).

Theoretically a voltage source must have zero output resistance and a load accepting a

signal in voltage form must have infinite resistance.

From the figure we can calculate the current delivered by the source and flowing through

the load:

Lout Rr

VI

+= and therefore the voltage across the load is:

VRr

RIRV

Lout

L

LL

+== a fraction of the voltage delivered by the source.

For 100% voltage delivery the load resistance RL must be much larger than the rout.

Ideally RL must be infinite and rout zero.

CURRENT SOURCES.

A current source (supply) is a device that delivers a fixed current difference at a load

independent on the resistance of the load RL.

The voltage appearing across the load (and

supplied by the current source) is calculated

with the aid of Ohm’s Law and the

resistance of the load.

A practical Current Source has a finite

output resistance Rout and can be

approximated with an ideal current source in

parallel with the output resistance Rout of the

non ideal supply.

A good current source must have an output

resistance much larger than the load

resistance in order for the current through

the load to be independent of the load itself

and to approach the current delivered by the

current source.

Moreover a load that accepts an input signal in current form must have a resistance much

smaller than the output resistance of the signal source (current source). Theoretically a

current source must have infinite output resistance and a load accepting a signal in

current form must have zero resistance.

From the figure we can calculate the voltage difference appearing between the leads A

and B of the load:

( )Lout

outL

LoutABRR

RIRRRIV

+== // and therefore the current flowing through the load is:

IRR

R

R

VI

Lout

out

L

AB

L

+== a fraction of the current delivered by the source.

For 100% current delivery on the load the load resistance RL must be much smaller than

the Rout. Ideally RL must be zero and Rout infinite.

VOLTAGE DIVIDERS.

A voltage divider is two resistors in series connected to a voltage source. Portion of the

voltage delivered by the source appears across

each resistance and therefore two resistances in

series constitute a practical way to supply to a

load a smaller voltage than the voltage delivered

by the source. The setup is illustrated at the

figure.

We can calculate the voltage difference between

points A and B by employing Kirchoff rules.

( )L

LRRR

VIRRRIV

////

21

21+

=⇒+=

and therefore the voltage delivered to the load is:

( )

+=⇒=

L

L

LLLRRR

RRVVRRIV

//

////

21

22

where L

LL

RR

RRRR

+=

2

22 //

We can see that the load resistance affects the operation of the voltage divider and

therefore the load voltage.

CURRENT DIVIDERS.

A current divider is two resistors in parallel connected to a current source. One of these

two resistors is the load. Only a portion of the current delivered by the source flows

through each resistance and therefore two

resistances in parallel constitute a practical

way to supply to a load a smaller current than

the one delivered by the source. The setup is

illustrated at the figure.

We can calculate the current flowing through

the load resistance RL by employing the rules

of Kirchoff. The voltage across the load is:

( )

+=⇒=

L

L

LLLRR

RRIVRRIV //

Therefore the current through the load is:

+=⇒=

L

L

L

L

LRR

RII

R

VI a fraction of the current delivered by the source. In practice

R contains the effects of the finite output resistance of the current source appearing in

parallel with any externally connected resistance to the source output.

THE THEVENIN EQUIVALENT CIRCUIT.

Consider an electronic device shown in the figure below. The device is shown as a “black

box” totally opaque to the user internally containing an unknown number and type of

electronic components. The complexity of the enclosed circuit is also unknown.

Terminals A and B interface the device with the external world and could serve either as

input or as output.

The Thevenin theorem states that the circuitry between terminals A and B internal to the

box can be replaced with the equivalent Thevenin circuit, a perfect voltage source

supplying a voltage called the Thevenin voltage (VTh) in series with a Resistance called

the Thevenin (sometimes called also the “input” or “output”) resistance depending on

weather terminals A and B serve as device input or output). The figure shows the

equivalent Thevenin circuit between terminals A and B replacing the internal components

of the device.

Rules for finding the Thevenin Voltage:

The Thevenin voltage (VTh) is the voltage difference between the terminals A and B

when they are open (and therefore no current flows into our out from the device).

Here are some basic procedures to find the Thevenin Resistance:

Method 1:

Short Terminals A and B and measure the current flowing through shorted terminals A

and B, Ishort. This current is also called the Norton current IN. The Thevenin Resistance is

the Thevenin Voltage divided by the current through the shorted terminals A and B

short

Th

ThI

VR =

Method 2:

Replace all Voltage Sources with a closed switch (short) and all Current Sources with an

open switch. The equivalent net resistance “seen” between terminals A and B is the

Thevenin Resistance.

Method 3:

Suppose you want to measure the input (or output) Resistance of a device. Ground the

output (or input if you are measuring the output resistance) and plug an ideal voltage or

current source at the terminal. Calculate the current supplied by the hypothetical ideal

voltage source or the voltage supplied by the hypothetical ideal current source if you

decide to go with a current source. Use Ohm’s law to calculate the resistance seen by the

source between the terminals.

Method 4:

Measure with a voltmeter the voltage between the terminals A and B. The voltmeter has

infinite resistance (it draws no current from the device) and therefore it registers the

Thevenin Voltage. Plug a load variable resistance RL between the terminals A and B (use

a potensiometer for this). With a voltmeter measure now the voltage drop across the load

resistor. With a screwdriver vary the value of the resistor until the voltmeter registers a

voltage drop across the load equal half the value of the already measured Thevenin

voltage. What is the relationship between the value of that load resistance and the

Thevenin Resistance between terminals A and B. Hint: The circuit is essentially a

voltage divider where the Thevenin Voltage is split on the Thevenin Resistance and on the

Load resistance.

THE NORTON EQUIVALENT CIRCUIT.

Consider the same electronic device shown in the figure below once more. The device is

again shown as a “black box” totally opaque to the user, internally containing an

unknown number and type of electronic components. The complexity of the enclosed

circuit is also unknown. Terminals A and B interface the device with the external world

and could serve either as input or as output.

The Norton theorem states that the circuitry between terminals A and B internal to the

box can be replaced with the equivalent Norton circuit, an ideal Current Source supplying

an electric current called the Norton (IN) in parallel with a Resistance called the Norton

(sometimes also called the “input” or “output”) resistance depending on weather

terminals A and B serve as device input or output.

The Norton Resistance RN is the same as the Thevenin Resistance discussed

above and therefore we already know how to find it (RN = RTh).

The figure shows the equivalent Norton circuit between terminals A and B

replacing the internal components of the device.

Rules for finding the Norton Current:

The Norton current is the current flowing through the terminals A and B if we short them.

(It is the Ishort current we used in the Thevenin theorem discussion to find the RTh).

USAGE OF NORTON AND THEVENIN CIRCUITS.

The Thevenin and Norton equivalent circuits are being used to determine how two

electrical or electronic components behave when they interact that is when they are

connected in such a way so that the output of the first becomes the input of the second.

Consider the situation shown in the figure below where device A (say a sensor or

detector) delivers its signal to device B (say an Amplifier). Device A is considered a

voltage source (the output information is supposed to be the voltage) and device B is a

voltage Amplifier (expects a voltage signal at its input). The output of device A (the

sensor) has been replaced with its equivalent Thevenin Circuit, there the Thevenin

voltage is the signal VS and the Thevenin Resistance is the output resistance of the

detector say Rd. The input of the amplifier has been replaced by its Thevenin rinput

Resistance say Rin. On the Amplifier input side there is no signal therefore there is no

Thevenin Voltage or Norton Current source.

We can recognize immediately the action of the voltage divider and the signal which

really appears at the input of the Amplifier and being Amplified is:

+ Din

in

SRR

RV

which is a fraction of the useful voltage delivered by the sensor.

For good “matching” of the two electronic devices we want this fraction to approach

100%, that is we need Rin to be much larger that RD. Ideally we want the voltage source

to have zero output resistance and the device accepting voltage signals to have infinite

input resistance.

Consider now the situation shown in the figure below where device A (say a sensor or

detector) delivers its signal to device B (say an Amplifier). However now device A is

considered a current source (the output information is supposed to be encoded in the form

of current) and device B is a current Amplifier (expects a current signal at its input). The

output of device A (the sensor) has been replaced with its equivalent Norton Circuit,

there the Norton Current is the signal IS and the Norton Resistance (same as the Thevenin

resistance) is the output resistance of the detector say Rd. The input of the amplifier has

been replaced by its Thevenin (or Norton) input Resistance say Rin. On the Amplifier

input side there is no signal therefore there is no Thevenin Voltage or Norton Current

source.

We can recognize immediately the action of the current divider and the signal which

really flows through Rin at the input of the Amplifier and therefore being Amplified is:

+ Din

D

SRR

RI

which is a fraction of the useful Current Signal delivered by the sensor.

For good “matching” of the two electronic devices we want this fraction to approach

100%, that is we need Rin to be much smaller that RD. Ideally we want the current source

to have infinite output resistance and the device accepting current signals to have zero

input resistance (effectively shorted inputs).

We see therefore that the practical usage of the Norton and Thevenin equivalent circuits

in electronics is to determine how two circuits interact when they are connected and

signals are propagating through them.

We can model the input and/or the output of a device either with its Norton or with its

Thevenin equivalent circuits. The Norton and the Thevenin resistances are the same ant

the Thevenin voltage is related to the Norton current via the formula:

ThNThNTh RRRIV ==

The results of our analysis will be the same and independent on our choice to model it

using the Thevenin or the Norton equivalent circuit.

However we need to decide if we will consider the output of a device a signal or a current

source based on the output resistance as well as we need to decide if the input of a device

is accepting signals in voltage or in current form base on its input resistance. It is the

responsibility of the experimentalist and the designer to make a good matching of the

components.

THE OPERATIONAL AMPLIFIER (Op Amp)

An Operational Amplifier (otherwise called op-amp) is a Differential Amplifier

incorporated in a chip as a linear integrated circuit. The Differential Amplifier is an

Amplifier which amplifies the

difference between two signals

applied to the two inputs it has. The

two inputs are indicated with the

symbols:

+ (plus) or the non inverting input or

υ+ and

-- (minus) or the inverting input or

υ--

The output signal can be written

as: ( )−+ −⋅= υυυ Aout

The gain A is a very large number

usually between 150,000 and

300,000.

In the figure we show the schematic diagram for an op amp as it appears in electronic

circuit designs.

The most widespread op-amp chip is the LM741

which incorporates a single amplifier per chip.

The experimentalist should always study the

data sheet of the LM741 chip for the correct

specifications and pin-out usage.

In order for the chip to work it needs to be

powered by a positive and a negative power

supply, indicated by +Vcc and –Vcc in the

figure. Their values need not be the same but for

most cases we select +12V and -12V (or +15V

and -15V). The pin out diagram appears in the

Figure. Pin NC is left unconnected. For basic lab experiments the OFFSET NULL pins

will be left unconnected too.

Note: The op-amp cannot deliver an output voltage outside the +Vcc and –Vcc

range. Also the op-amp cannot deliver an output current larger than a value

specified at its data sheet (15 mA or 20mA for the LM741 chip). The chip clips the

output voltage and the output current at their limit values.

The LM741 has been designed

to appear in linear Op-Amp

Circuits with negative

feedback. That is when we

design electronic circuits

involving the 741 op-amp a

portion of its output is fed at

the inverting input (negative

feedback), via passive elements

(usually Resistors and/or

Capacitors)

An example of such a circuit

appears in the figure.

In order to analyze such circuits we follow the following three Op-Amp rules:

Rule 1: The Op-Amp has infinite input impedance and no current is flowing into it.

Rule 2: The Op-Amp with a negative feedback at a linear electronic circuit works in such

a way so that, both inverting (minus) and non-inverting (plus) inputs are held at the same

voltage. For Example in the figure the inverting input is held at zero voltage (virtual

ground) by virtue of the non inverting input that is hardwired at the ground.

Rule 3: Rule number 2 does not hold if the output voltage or if the output current ar out

of their limits (their specs). They cannot be out of their limits. Simply the chip clips the

output voltage (or the output current) at their limiting values whatever the input voltages

at the inverting and non inverting inputs may be.

These rules allow us to analyze almost all linear circuits containing op amps and calculate

the output voltage as a function of the input (the gain for the circuit).