1 Laboratory 4 Building and measuring circuits on the breadboardham.elcom.pub.ro › metc › platf...

Measurements in Electronics and Telecommunications – Lab. 4 -online- rev. 1.4 1

Laboratory 4

Building and measuring circuits on the breadboard

Purpose: Experiments on circuits built on a breadboard. Measurement of resistive

dividers using the ohmmeter and the oscilloscope.

Summary of theory

1. Reading and measurement of resistors

The values of resistances are either clearly written on the resistor or encoded

using the color code (figure 1).

Figura 1: The color code for resistors; examples with 4 and 5 colored bands

The number of colored bands drawn on a resistor is variable, depending on how

many significant digits are marked (2 or 3):


- the resistance is written as MN•10K sau MNP•10K hence resulting 2 or 3 bands

for the value and always one more band for the multiplier (resulting a total of 3

or 4 bands);

- the tolerance is the 4th or the 5th band; if it is missing (3 bands in total), the

tolerance is considered +/-20%.

How do we know if we hold the resistor correctly before reading?

- usually, the value and multiplier bands are grouped together and there is a

noticeable space between this group and the solitary tolerance band. The

tolerance band should be held to the right;

- usually, the band corresponding to the first digit is the closest to an end;

- the most common values for tolerance (marked with gold and silver bands, 5%

and 10%) are represented by colors that cannot be the first digit (there is no value

for gold and silver).

2. Breadboard description

The solderless breadboard or protoboard (fig. 2) allows interconnecting

electrical components without soldering. It contains a matrix of holes into which wires

and the leads of components can be inserted. Vertical 5-hole groups are interconnected

inside the board with spring clips. These clips are often called tie points or contact

points. The entire area of 5-hole groups is called a terminal strip. There are also 2

horizontal 25-hole rows, on each of the long sides, that are interconnected. These are

called bus strips and are usually used as power lines. A detail of this is given in figure

2, where the board is partially transparent (the straight lines represent the clips and

conduct electricity).

Figure 2: Breadboard (up) and its internal connections (below). Straight line = electrical

connection


A detail of the internal contacts (metalic clips) that make possible the electrical

connections is shown in figure 3.

Figure 3: Breadboard: internal contacts

The 2 wires are electrically connected by connecting them in the same group of 5 connection points

Notice how, in the center of the board, a groove runs parallel to the long side.

This groove (between rows “E” and “F” on fig. 3) separates the 5-holes groups.

Fig. 4 shows two examples of how to construct simple circuits: 3 resistors

connected in series (left) and 3 resistors connected in parallel (right). Notice how the

groove in the middle of the board acts as a separator. The 5-hole groups above the

groove are not connected with the 5-hole groups below the groove – otherwise, for the

parallel circuit, the resistances would have been in short-circuit.

Figure 4a: series connection Figure 4b: parallel connection


Figure 5: another example of connecting 2 resistors in parallel – photo

Remark: never place both terminals of a component in any 2 connection points

from the same group of 5 holes! This would mean to short-circuit the component! (see

figure 6)

Figura 6: wrongly connected component, in short-circuit (left) and the equivalent schematic

diagram (right)

3. The Breadboard Simulator software

Download Breadboard Simulator from the following link: https://ds0.me/csim/.

To be able to use the simulator, the contents of the downloaded .zip file should be

extracted in a folder in your computer. Start the software by running

BreadboardSim.exe.

Breadboard Simulator is a program that allows the simulation of a breadboard

like the one available in the laboratory, described above in the theoretical summary. The

graphical user interface (GUI) of the program is shown in figure 7. It can be observed

that a breadboard is illustrated in the main screen. Components that can be used to build

circuits are available on the left side of the interface.

The holes of the breadboard shown in the simulator are connected like in the case

of a real breadboard, as described above. The vertical 5 holes groups are electrically

connected. The holes placed on each of the horizontal rows at the top and the bottom of

the breadboard are also interconnected, just as it was already described.


Figure 7: The user interface of the Breadboard Simulator program

It is recommended to use the horizontal rows placed on the top and bottom edges

of the breadboard as power lines. The power supply should be connected in these rows.

The program automatically does this by default. The horizontal red line in the upper part

of the breadboard highlights that all the holes in the corresponding horizontal row are

connected to the positive (+) terminal of the power supply (by default, a 5V power

source is used). In the bottom part of the breadboard, two horizontal rows can be found,

one marked with black and the other marked with blue. All the holes in the horizontal

row next to the black line are connected to Ground (0V). Similarly, all the holes in the

horizontal row next to the blue line are connected to the negative terminal of the power

source (-5V), which is not used in this laboratory.

3. Resistive voltage dividers

a) b)

Figure 8: Resistive voltage dividers with 2 resistors (left) and with 3 resistors (right)

The circuits illustrated in the two schematic diagrams shown in figure 8 are called

resistive voltage dividers because they allow the division of voltage by using resistors.

As it can be observed in figure 8, in both circuits the resistors are connected in series.

In figure 8a (left side), the two resistors denoted with R1 and R2 are interconnected in

point B. The second terminal of R2 is connected to the ground ( ). Similarly, in figure

8b (right side) R1 and R2 are interconnected in point B, R2 and R3 are interconnected in


point C, and R3 has the second terminal connected to the ground ( ). The arrows show

that both UA and UB voltages are measured with respect to the same ground terminal

( ). In this way, the voltage UA=VA – VGND=VA, where VGND is the potential of the

ground (0V), and UB=VB-VGND=VB.

In figure 8a, the resistors are connected in series, therefore the current that flows through

R1 and R2 is the same. Denoting with U1,2 the voltages over R1,2 respectively, it results:

=

+

= ∙

∙ + ∙

=

+

Therefore, the division ratio can be determined either by measuring the

resistances or by measuring the voltages.

For the circuit shown in figure 8b, the voltage ratio can be found in a similar

manner, because the current flowing through the three resistors is also the same (series

connection):

= +

+ +

= +

+ +

The ratio between U2 and UA can also be found similarly:

=

+ +

=

+ +

In this case, if the division ratio is determined by measuring the two voltages

using the oscilloscope, a problem will arise when measuring U2. It should be observed

that the voltage denoted with U2 is represented by the difference of two potentials, both

different from zero!

U2 = VB – VC = UB – U3

The potentials denoted with VB and VC are both different from zero. Therefore,

U2 is not measured with respect to the ground, like in the previous examples. It is the

voltage between two points (B and C), none of them being a ground termination. The

oscilloscope can only be used to directly measure voltages with respect to the ground

potential (the 0V, reference, potential) because one of the two terminals of each

oscilloscope’s input (usually marked with black) is connected to the ground (the metallic

coating of the BNC connector is connected to the device’s ground). Therefore, U2 will

not be measured directly. UB and U3 (or VB and VC) can be directly measured (because

they are measured with respect to the ground). U2 will then be found by subtracting U3

from Ub. This method of measuring the voltage between any 2 points, none of them

being grounded, is also called differential measurement.

Always connect a real oscilloscope’s ground connection (black alligator clip) only

to the ground of the circuit!

OBS: this is necessary for any device that has BNC input connectors (the connector of the oscilloscope

and signal generator), because the metallic outer terminal of these jacks is already internally

connected to the device ground. The devices that have a differential input do not use this type of

connector – see, for example, the digital voltmeter in the laboratory!


4. The LM555 astable circuit

Signal generators are not available in Breadboard Simulator. Integrated circuits

(IC) that are available in the program’s library will be used to generate signals. In this

laboratory, the 555 integrated circuit in the astable configuration will be used to generate

a rectangular signal (square wave). In this configuration, the 555 IC works as an

oscillator, generating a signal that switches between two voltage values. This is the

reason why this configuration is called astable (none of the two output values is

continuously held constant - stable, but they are switched). In contrast, a bistable circuit

is continuously in one of the two stable states, and the switching between the states is

done using an external command. The astable configuration of the 555 IC

(https://en.wikipedia.org/wiki/555_timer_IC [1]) is shown in figure 9a (left) and in figure 9b

(right) two waveforms for this configuration are shown: the output signal and the

voltage across the capacitor C.

a) b)

Figure 9: a) The 555 IC astable configuration, b) Important waveforms for the 555 astable

configuration

It can be observed that the output signal is a rectangular signal and that the switching

between the two output voltage values is done using the voltage on the C capacitor. The

capacitor is successively charged and discharged. This voltage controls a bistable circuit

inside the 555 IC. The capacitor is charged from the power supply denoted with VCC

through the resistors R1 and R2, or it discharged to ground through the R2 resistor. The

pin number 7 of the IC (DIS) is connected to ground when the output voltage is switched

to zero.


a) b)

Figure 10: a) The 555 IC pinout, b) The placement of the 555 IC on the breadboard

OBS: The pins of any integrated circuit are numbered in order, pin number 1 being the one on the left

of the key mark on its body (circular, semi-circular, square mark), as seen in figure 10a). It can be

observed that in figure 9a, the pin layout does not correspond to the pin layout of the real component.

This representation was chosen so the schematic diagram will be easy to read. This is also highlighted

by the fact that the mark corresponding to pin 1 is missing from figure 9a.

In figure 10b) it is illustrated how the 555 integrated circuit is connected on the

breadboard. It can be seen that the pin number 1 (GND in figure 9a) is connected to the

ground (remember that the ground potential is available in any hole of the horizontal

row on the bottom edge of the breadboard, next to the black line), and pin number 8

(VCC in figure 9a) is connected to the power supply, VCC (available in any hole of the

horizontal row on the top of the breadboard, next to the red line). It can also be observed

that the pins are numbered in order, starting with pin 1 on the left side of the key mark

on the IC body.

The functioning of the astable configuration is controlled by the R1 and R2

resistors, as well as by the capacitor C. It can be shown that the frequency of the

rectangular signal generated by the circuit is found using the following formula:

=1

ln2 + 2

where ln is the natural logarithm, with ln(2) ≅ 0.693.


Measurements

Compute the ID identifier based on the sum of the ASCII codes (http://www.asciitable.com/)

of the first name and last name initials (uppercase letters) Ni of the team members; take the remainder

after division of the sum with 100 and add 1.

- N1,2,3,4,… = ASCII codes of the initials (uppercase)

- ID= ∑ mod 100 +1

- for example, team members: Dorel Ionel Vasilescu and Ion Ionescu = D,I,V,I,I:

N1=ascii(“D”) = 68; N2=73; N3=86; N4=73; N5=73;

- 68+73+86+73+73 = 373;

- ID = 373 mod 100+1 = 73+1=74

1. Getting to know Breadboard Simulator

1.a) Checking Ohm’s law

Using Breadboard Simulator, the circuit shown in figure 11 will be built on the

breadboard: a resistor connected to the power supply and to the ground.

• R = the closest value to (10+ID)/ 10 that is available, in KΩ

• Ex: ID = 74 Rcomputed=84/10=8.4KΩ Rchosen =10KΩ

Using the color code, determine the resistance value and the tolerance.

Figure 11: The circuit for checking the Ohm’s law

The terminal of the resistor denoted with A is connected to the power supply: for

this, the Place Wire (Ctrl+W) icon is selected and then a connection is made between

one of the holes in the 5 hole group containing the A terminal and the top horizontal

row next to the red line. After the connection has been made, the placed wire will be

colored in red, showing that the wire is connected to the power supply. In a similar way,


the B terminal of the resistor will be connected to the ground (bottom horizontal row

next to the black line). In this case the wire is colored in black, showing that the wire is

connected to the ground. Attention, use the horizontal row next to the black line (ground,

0V), not the blue line (-5V)!

After starting the simulation (pressing the play button, Run), the voltage and

current in various points of the circuit can be found by hovering the cursor over the

respective point. Using this method, find the voltage and current in point A. Remark: just like it was mentioned earlier, the voltage that is measured is with respect to the ground,

thus corresponding to the measurement done with an oscilloscope or voltmeter that has the second

terminal connected to the ground. This second terminal is not drawn to avoid overloading the drawing.

Using the Ohm’s law, find the resistance value.

b) Repeat the measurements (the value of the resistance using the color code, finding

the resistance using the Ohm’s law) for a randomly chosen resistor from the program’s

components library.

2. Studying the connections on the breadboard by building and measuring resistive

dividers

2a) Resistive voltage divider built with two resistors

Using Breadboard Simulator, build on the breadboard the resistive divider

illustrated in figure 8a.

For this circuit, two resistors having the resistance value equal to 1kΩ will be

used. The components can be found in the program’s library on the left side of the user

interface. The resistors should be placed so they will be connected in series. In figure

12a, the interconnection of the two resistors is done in point B. It can be seen that the

second terminal of R1 is connected to the first terminal of R2, because they are connected

in the holes from the same 5 holes group, that are interconnected on the back of the

breadboard, as shown in the summary of theory.

The first terminal of R1 resistor, point A, is connected to the power supply: for

this, the Place Wire (Ctrl+W) icon is selected and a connection is made between one of

the holes in the same 5 holes group that contains point A (the first terminal of R1) and

one hole from the horizontal row of holes on the top of the breadboard, next to the red

line. After this operation has been done, the wire should be colored in red to highlight

the connection to the power supply. In a similar manner, the second terminal of R2 will

be connected to the ground. In this case, the wire will be colored in black, highlighting

that the wire is connected to the ground (zero potential).

After the circuit has been built, the simulation is started by pressing the Run

button (play symbol), from the program’s command toolbar.

After the simulation has been started, by placing the cursor over a connection, the

current and the voltage in that point can be measured. Thus, in point A the voltage

should be 5V (the default power supply voltage), and a current equal to 2,5 mA. Because

the two resistors are connected in series, the equivalent resistance between the power

supply positive terminal and the ground is equal to 2kΩ. It results that the current that


flows through the two resistors is equal to I=5V/2kΩ = 2,5 mA. In point B on figure

12b, the voltage is equal to 2,5V. It can be observed that:

=2,5

5=

1

2=

+

The experiment described above is repeated choosing different values for R1 and

R2. The voltages UA, UB, UA/UB will be marked on the worksheet, as well as the division

ratio computed using the resistance values of the chosen components. The available

resistance having the closest value of the one computed based in the ID will be chosen:

• Set 1: R11 = ID*10 [Ω] R21= ID*25 [Ω]

• Set 2: R12 = (170-ID)/15 [KΩ] R22= (130-ID) /12 [KΩ]

a) b)

Figure 12: a) Building the circuit shown in figure 8a, b) The voltage and current in point B

2b) Resistive voltage divider built with three resistors

Proceeding as in 2.a, the circuit shown in figure 8b will be built on the breadboard.

The values of R1, R2 și R3 will be chosen as the closest values to:

• R1 = (170-ID)/15 [KΩ] R2= (130-ID) /12 [KΩ] R3= (105-ID)/8 [KΩ]

Using the color code, find the resistance values of R1, R2 și R3 and their tolerances.

Based on the measured values of UA, UB și UC the measured values of UB/UA and U2/UA

are determined. The computed values UB/UA and U2/UA, based on the values of the

resistances R1, R2 și R3 are also determined.

3. Building given circuits on the breadboard

For each of the circuits in figure 13:

• R1 = ID*100 [Ω] R2= ID*250 [Ω]


- compute the equivalent resistance between points A and B, according to the nominal

values (chosen from the list available in the program) of the resistances in the circuit.

- build the circuit on the breadboard and draw the way it was done on your worksheets

(OBS: obviously, there is no unique solution); write the values of the resistances next

to the resistor symbols!) Indication: The drawing can be done by any means, including drawing by hand over the picture of the

empty breadboard, photographing the final result and inserting it as an image in the corresponding

place in the worksheet, but the values of the resistances on the diagram must be clearly visible!

- measure the resistance between points A and B by connecting point A to the power

supply and point B to the ground. Proceeding as in point 1, determine the voltage and

the current in point A and use the Ohm’s law to find the equivalent resistance.

Indication: you are not required to compute the relative error, but if the measured value differs from

the computed value by more than a few percent, it is more than likely that there is an error, either in

your calculations or in the way you built the circuit; find and eliminate the mistake!

circuit 1 circuit 2 circuit 3 circuit 4

Figura 13: circuits to be built on the breadboard

4. Designing and building resistive circuits on the breadboard

Design circuits built with resistors as described further:

- for each of the desired (target) values of RAB from table 1, design a circuit using only

resistors with the resistance values R1, R2 chosen at point 3 in such way that the

computed equivalent resistance of the designed circuit should have a maximum +/- 10%

deviation from the target value. Draw the schematic on the worksheet.

- build the circuit on the breadboard and draw it on your worksheet (including the choice

of points A and B and the values of the resistors).

- use the simulator to measure the obtained RAB value to confirm the correctness of the

computation and of the circuit.

circuit RAB desired (target)

1 ID*100 [Ω]

2 ID*320 [Ω]

3 ID*560 [Ω] Table 1


5. Study of the response of the RC circuits to the rectangular signal

5.a) Study of the 555 integrated circuit in the astable configuration with

predefined values

From the menu toolbar of Breadboard Simulator select File->Sample Circuits-

>555 Timer->Astable. The program automatically builds on the breadboard the circuit

from figure 9 (555 circuit in astable configuration) with predefined values. The only

differences between the circuit automatically built on the breadboard (figure 14) and the

circuit shown in figure 9 are:

• On the breadboard there is an extra 10 µF capacitor connected between the pin

number 5 of the 555 IC and ground.

• On the breadboard, between the output of the 555 and ground we can find a

resistor and an LED connected in series, with the role to show the correct

functioning of the circuit. They have no influence on the circuit’s functioning.

During the circuit simulation, the LED should blink with the corresponding

frequency. The negative terminal (the cathode) of the LED and electrolytic

capacitor are marked using a cutout.

Figure 14: The 555 IC in the astable configuration built on the breadboard - example

Verify that the circuit illustrated on figure 9a is correctly built on the breadboard.

Identify R1, R2 and C and determine the resistance values of the resistors using the color

code. Find where the two oscilloscope probes are connected.

Start the simulation. Measure the output signal’s frequency using the Graph View

(figure 15). Compute the theoretical value for the frequency using the formula given in

the theory summary.

Write the two values, fmeasured și fcomputed on the worksheet.


Figure 15: The image shown by the Graph View during the simulation

5.b) Study of the 555 integrated circuit in the astable configuration with

given values

Choose from the simulator’s library components with values closest to:

• R1= ID [KΩ] R2= 1.5*ID [KΩ] C=(101-ID) [µF]

Modify the circuit so the new components, selected above, are used. Repeat the

simulation and measurements done at the previous point.

5.c) Study of the response of the RC integrator circuit to a rectangular signal

generated using the 555 integrated circuit

To increase the oscillation frequency of the astable circuit in the kHz range, the

values for R1, R2 and C in figure 14 will be replaced with the following values (note that

the required capacitor is not electrolytic):

• R1= ID [KΩ] R2= 1.5*ID [KΩ] C=(101-ID) [nF]

The simulation parameters need to be changed. Press the Settings icon in the

instrument toolbar (figure 16a).

In the Circuit Settings window, set the Simulation Speed parameter at a value

equal to 1 ms or comparable with the period of the studied circuit’s output signal. In the

Graph View window, press the Settings button in the bottom-right corner (figure 16 b)

and set the horizontal display coefficient, Sec/div, at a value around 1ms (choose the

appropriate value to see a few periods of the signal).

Compute and measure the oscillation frequency. Write the two obtained values

on the worksheet, fmeasured și fcomputed.


a) b)

Figure 16: a) The Circuit Settings windows, b) The Graph Setting window

On the breadboard, in the unoccupied right side, build the RC integrator circuit

(LPF) studied in laboratory 3, connected to the output of the astable circuit (replace the

circuit represented by the resistor and LED connected in series. The LED blinking

cannot be observed anyway because of the high frequency). The values for the two

components of the integrator circuit, the R0 resistor and the C0 capacitor, will be chosen

so the cutoff frequency of the R0C0 circuit will not deviate more than +/- 50% from the

frequency of oscillation of the astable circuit. Write the chosen R0 and C0 values and the

cutoff frequency of the R0C0 circuit.

Visualize and draw on the worksheet (eventually by capturing the Graph View

image) between two and three periods of the displayed signals. On the drawing in the

worksheet, the Sec/div that was used needs to be specified.

5.d) Study of the response of the RC differentiator circuit to a rectangular

signal generated using the 555 integrated circuit

Proceed like at the previous point to find the response of the RC differentiator

circuit (HPF) to a square wave. For this, the R0 and C0 components on the breadboard

should be interchanged. Run the simulation and draw the new two signals. Also, the

Sec/div coefficient that was selected needs to be written on the worksheet.


Preparatory questions

1. For the voltage divider in the figure, R1=1K, R2=2K, R3=3K,

R4=4K. Compute the ratio: a) U3/UA; b) U3/U4. 2. Define the nominal value of a resistor.

3. Explain what a differential measurement means and give an

example for its utility.

4. Knowing the

value (in KΩ) for

the resistors in the circuit in the figure, built on a

breadboard, compute the equivalent resistance

between A and B.

5. Connecting the terminals of a resistor R at 2 holes

of the same vertical group of 5 holes of a breadboard,

which is the value of the measured resistance, using

an ohmmeter?

6. Which is the type of measurement not allowed by

a meter using BNC input terminals?

7. The voltage between A and B on the figure is UAB=10V. Which

is the value for the voltage drop on R1 in the two cases?

8. Define the tolerance of a resistance (formula). How is it marked

on the resistor?

9. On a voltage divider used to determine the oscilloscope’s input resistance: a) using R1=1MΩ, the

amplitude measured on the screen is half of the amplitude from the generator. Compute Ri. b) using

R1=Ri/5, the amplitude from the generator is 10V. Determine the amplitude displayed on the scope.

10. Explain what would happen if the oscilloscope’s input resistance would be infinite; which would

be the value of the ratio between the value measured on the display of the oscilloscope and the one

from the generator?

11. With resistors R1=5KΩ and R2=2KΩ (as many as you wish), design and draw the schematic with

equivalent resistance: a) RAB=4.5 KΩ; b) RAB=11 KΩ. Draw the connections necessary on a

breadboard.

12. Define the transfer function of a two-port circuit. Determine the

transfer function for the two-port in the figure

13. Compute the equivalent resistance (AB, CD respectively) of the

circuits in the figure. Hint: RAB=∞, RCD=0

1 Laboratory 4 Building and measuring circuits on the breadboardham.elcom.pub.ro › metc › platf...

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Transcript of 1 Laboratory 4 Building and measuring circuits on the breadboardham.elcom.pub.ro › metc › platf...