UNIVERSITY POLYTECHNIC A. M. U., ALIGARH

UNIVERSITY POLYTECHNIC A. M. U., ALIGARH

Teacher’s Signature BEE-691

Electronics & Control Lab - II

EXPERIMENT No.: ____

Name: ___________________________

Class: Diploma in Electrical Engg., VI^th Sem

College No.: ____________________

En. No.: _______________________

Group No: _____________________

Partners of Group:

1. _________________________

2. _________________________

3. _________________________

4. _________________________

Date of performing Exp:____/____/____ Date of Submission of Report:____/____/____

Object:________________________________________________________________

______________________________________________________________________

Apparatus Used:

S. No. Lab No. Equipment Used Range Make

Observation Table/Circuit Diagram:

UNIVERSITY POLYTECHNIC A. M. U., ALIGARH

Teacher’s Signature

Name: ___________________________

Class: Diploma in E&I., VI^th Sem

College No.: ____________________

En. No.: _______________________

Group No: _____________________

Partners of Group:

1. _________________________

2. _________________________

3. _________________________

4. _________________________

Date of performing Exp:____/____/____ Date of Submission of Report:____/____/____

Object:________________________________________________________________

______________________________________________________________________

Apparatus Used:

S. No. Lab No. Equipment Used Range Make

Observation Table/Circuit Diagram:

VI Semester Diploma Engineering (Electrical / Instrumentation)

Electronics & Control Lab-II.

BEE-691

1. To obtain the V-I Characteristics of SCR and to determine the latching current, holding current.

2. (a) To observe the output waveforms of resistance firing circuit of SCR and plot the "gate current vs anode current" characteristic of the SCR.

(b) To study and plot phase firing characteristics of an SCR.

3. To study speed control of Universal motor using Triac.

4. (a) To determine experimentally the transfer function of the given lead compensating network.

(b) Obtain its frequency response for its magnitude (dB) and phase (degrees). (c) To verify the same using the theoretical analysis.

5. (a) To determine experimentally the transfer function of the given lag compensating network. (b) Obtain its frequency response for its magnitude (dB) and phase (degrees). (c) To verify the same using the theoretical analysis.

6. (a) To plot the different wave shapes for OP-AMP based differentiator.

(b) To plot the different wave shapes for OP-AMP based integrator

7. To study the Time Response of a Second Order series RLC System to determine the parameters of L & C from unit step input.

General Instructions to students for Electronics and Electrical Engineering Lab courses

 Be punctual to the lab class.

 Attend the laboratory classes wearing the rubber sole shoes.

 Avoid wearing any metallic rings, etc. as they are likely to prove dangerous at times.

 Boys students should tuck in their uniform to avoid the loose cloth getting into contact with rotating machines.

 Acquire a good knowledge of the surrounding of your worktable. Know where the various live points are situated in your table.

 In case of any unwanted things happening, immediately switch off the mains in the worktable.

 This must be done when there is a power break during the experiment being carried out.

 Before entering into the lab class, you must be well prepared for the experiment that you are going to do on that day.

 You must bring the related text book which may deal with the relevant experiment.

 Get the circuit diagram approved.

 Make connections as per the approved circuit diagram and get the same verified. After getting the approval only supply must be switched on.

 Get the reading verified.

 You must get the observation note corrected on completion of experiment. Write the answer for all the discussion questions in the observation note

 Submit the record note book for the experiment completed in the next class.

 If you miss any practical class due to unavoidable reasons, the missed experiment can be performed (if time permits) after completion of the rotor. No experiment shall be performed after last day of semester

 Such of those students who fail to put in a minimum of 75% attendance in the laboratory class will run the risk of not being allowed for the University Practical Examination. They will have to repeat the lab course in subsequent semester after paying prescribed fee.

 Use isolated supply for the measuring instruments like CRO in Power Electronics Laboratory experiments.

Revised: February 2020

Experiment No: 1

Object: To obtain the V-I Characteristics of SCR and to determine the latching current, holding current.

Apparatus Required:

S.No. Name of the equipment Range/Specifications Qty Make

Fig. 1: Circuit diagram for SCR Characterstics Theory:

Silicon Controlled Rectifier: The Silicon Control Rectifier (SCR) consists of four layers of semiconductors, which form NPNP or PNPN structures. It has three junctions, labeled J1, J2, and J3 and three terminals. The anode terminal of an SCR is connected to the P-Type material of a PNPN structure, and the cathode terminal is connected to the N-Type layer, while the gate of the Silicon Control Rectifier SCR is connected to the P-Type material nearest to the cathode.

Fig. 2: Structure of SCR

Forward blocking mode: In this mode of operation the anode is given a positive potential while the cathode is given a negative voltage keeping the gate at zero potential i.e. disconnected. In this case junction J1 and J3 are forward biased while J2 is reversed biased due to which only a small leakage current flows from the anode to the cathode until the applied voltage reaches its breakover value at which J2 undergoes avalanche breakdown and at this breakover voltage it starts conducting but below breakover voltage it offers very high resistance to the flow of current and is said to be in off state.

Forward conduction mode: SCR can be brought from blocking mode to conduction mode in two ways - either by increasing the voltage across anode to cathode beyond breakover voltage or by applying of positive pulse at gate. Once it starts conducting no more gate voltage is required to maintain it in on state.

There is one way to turn it off i.e. Reduce the current flowing through it below a minimum value called holding current.

Reverse blocking mode: SCRs are available with reverse blocking capability. Reverse blocking capability adds to the forward voltage drop because of the need to have a long, low doped P1 region. (If one cannot determine which region is P1, a labeled diagram of layers and junctions can help). Usually, the reverse blocking voltage rating and forward blocking voltage rating are the same. The typical application for reverse blocking SCR is in current source inverters.

Latching Current: Latching current (IL) is the minimum principal current required to maintain the Thyristor in the on state immediately after the switching from off state to on state has occurred and the triggering signal has been removed.

Holding Current: Holding current (I_H) is the minimum principal current required to maintain the Thyristor in the 'ON' state.

Observation Tables:

I_G1 =

VAK (Volts) IA (mA)

IG2 =

VAK (Volts) IA (mA)

Model graph:

Fig. 3: V-I Characteristics of SCR

Procedure:

V-I Characteristics:-

1. Make all connections as per the circuit diagram of Fig. 1.

2. Initially keep V₁ & V₂ at minimum position and R₁ & R₂ maximum position.

3. Adjust Gate current Ig to some value (2.5/5.0 mA) by varying the V1 or R1.

4. Now slowly vary V2 and observe anode to cathode voltage VAK and anode current IA.

5. Tabulate the readings of anode to cathode voltage V_AK and anode current I_A.

6. Repeat the above procedure for different Gate current Ig.

Gate triggering and finding V_g and I_g:- 1. Keep all positions at minimum.

2. Set anode to cathode voltage V_AK to some value say 15V.

3. Now slowly vary the V1 voltage till the SCR triggers and note down the reading of gate current(IG) and Gate Cathode voltage(VGK) and rise of anode current IA

4. Repeat the same for different Anode to Cathode voltage and find V_AK and I_G values.

To find latching current:-

1. Keep R2 at middle position.

2. Apply 20V to the anode to cathode by varying V₂

3. Raise the Vg voltage by varying V₁ till the device turns ON indicated by sudden rise in I_A. The current, at which SCR triggers, is the minimum gate current required to turn ON the SCR.

4. Now, put OFF the gate voltage using S1 and set R2 at maximum position, then SCR should turn OFF, if it is not turning OFF then reduce V₂ till the device turns OFF.

5. Now decrease the R2 slowly, to increase the anode current gradually in steps at which it goes off.

6. At each and every step, put OFF and ON the gate voltage switches V1. If the Anode current is greater than the latching current of the device, the device stays ON even after switch S₁ is OFF, otherwise device goes to blocking mode as soon as the gate switch is put OFF.

7. If IA > IL then, the device remains in ON state and note that anode current as latching current.

8. Take small steps to get accurate latching current value.

To find holding current:-

1. Now increase load current from latching current level by varying R2 & V2

2. Switch OFF the gate voltage switch S1 permanently (now the device is in ON state)

3. Now increase load resistance(R₂), so that anode current starts reducing and at some anode current the device goes to turn off .Note that anode current as holding current.

4. Take small steps to get accurate holding current value.

5. Observe that I_H<I_L Precautions:

1. All the connection should be tight.

2. Ammeter is always connected in series in the circuit while voltmeter is parallel to the conductor.

3. The electrical current should not flow the circuit for long time, otherwise its temperature will increase and the result will be affected.

4. It should be cared that the values of the components of the circuit do not exceed to their ratings (maximum value).

5. Before the circuit connection it should be checked out the working condition of all the Components.

Result:

Report:

1. Define holding current, latching current, ON state resistance, breakdown voltage.

2. Write an expression for anode current?

3. Mention the applications of SCR?

4. What is the difference between an ordinary diode rectifier and SCR?

5. What will happen if gate current is reduced to zero after SCR has fired?

6. Describe the actual construction of an SCR.

Experiment No: 2 (a)

Object: (a) To observe the output waveforms of resistance firing circuit of SCR and plot the "gate current vs anode current" characteristic of the SCR.

Apparatus used:

S. No Lab No. Equipment Range/rating Qty. & Make Circuit Diagram

A

D1

15 V 2 V

0-25 mA

470 Ω To CRO 0-5 A

mA

100 kΩ A K G

~ ~

RL

R

Fig. 1: Resistance triggering circuit

Theory:

It includes one fixed resistor (R), variable resistor, diode, SCR(Silicon Controlled Rectifier), Load resistor (RL). The circuit diagram of an R Triggering consists of Simple resistor; diode combinations trigger and control SCRs over the full 180 electrical degree ranges, performing well at commercial temperatures. These types of circuits operate most satisfactorily when SCRs have fairly strong gate sensitivities. Since in a scheme of this type a resistor must supply all of the gate drive required to turn on the SCR, the less sensitive the gate, the lower the resistance must be, and the greater the power rating.

It provides phase retard from essential zero (SCR full “on”) to 90 electrical degrees of the anode voltage wave (SCR half “on”).Diode D1 blocks reverse gate voltage on the negative half-cycle of anode supply voltage. It is necessary to rate blocking to at least the peak value of the AC supply voltage and the trigger voltage producing the gate current to fire IGF are in phase. When EAC = Em, at the peak of the AC supply voltage, the SCR can still trigger with the maximum value of resistance between anode and gate.

Procedure:

1. Make the connections as shown in the circuit diagram of Fig. 1.

2. Adjust the 100K pot meter in its maximum value so the SCR does not fire.

3. Adjust the 100K pot meter slowly till the SCR fires; note the gate current and anode current.

Also observe the wave form on CRO.

4. Increase the gate current and note the variation in anode current.

5. Plot the characteristic taking anode current on Y-axis and gate current on X-axis.

6. Compare observed anode current with theoretical anode current.

Observations: V_m  2V_rms S.NO. Gate current

(mA)

Firing angle () From CRO

Anode current (mA) Theoretical

a (1 cos )

2

m L

I V

R 

  

Observed

Waveforms:

(a) (b) (c)

Fig. 4: Waveforms across gate, load and SCR for Resistance firing circuit of an SCR in a half wave circuit at (a) No triggering of SCR (b) α=90⁰ (c) α<90⁰

Vs = Source Voltage^; Vg= gate voltage; Vo = Output Voltage; VT = Thyristor Voltage.

Result:

Report:

1. What are the methods of firing in SCR? Explain the methods adopted in this experiment.

2. What are the limitations of R- firing and RC-firing?

3. Why an SCR is not firing at zero degree?

4. Why an SCR is not in conducting state during entire 180 degree?

VS

 2

3 4

t V sin tm 

Vg Vgt

t

t

t

t Vo

io VT

Vgp Vgp Vgt

R Large2

t

t

t

t

t

 2

3 4

V_S

Vg

Vo

io VT

Vgp=Vgt



270⁰

 2

3 4



90⁰ =90⁰

t

t

t

t

t

 2

3 4

VS

Vg

Vo io VT

<90⁰ Vgp>Vgt

Experiment No: 2(b) Object: To study and plot the phase firing characteristic of an SCR Apparatus used:

S. No Lab No. Equipment Range/rating Qty. & Make Theory:

The circuit with single SCR is similar to the single diode circuit, the difference being that an SCR is used in place of the diode. Most of the power electronic applications operate at a relative high voltage and in such cases; the voltage drop across the SCR tends to be small. It is quite often justifiable to assume that the conduction drop across the SCR is zero when the circuit is analyzed. It is also justifiable to assume that the current through the SCR is zero when it is not conducting. It is known that the SCR can block conduction in either direction. The explanation and the analysis presented below are based on the ideal SCR model.

A circuit with a single SCR and resistive load is shown in Fig.1.

Circuit Diagram:

Fig. 1

The source vs is an alternating sinusoidal source. If v_s = V_m sin(ωt), vs is positive when 0 < ω t < π, and vs is negative when π < ωt < 2π. When vs starts become positive, the SCR is forward-biased but remains in the blocking state till it is triggered. If the SCR is triggered at ωt = α, then α is called the firing angle. When the SCR is triggered in the forward-bias state, it starts conducting and the positive source keeps the SCR in conduction till ωt reaches π radians. At that instant, the current through the circuit is zero. After that the current tends to flow in the reverse direction but the SCR blocks conduction. The entire applied voltage now appears across the SCR. The various voltages and currents waveforms of the half-wave controlled rectifier with resistive load are shown in Fig.2 for α=40°.

Fig. 2. Various voltages and currents waveforms for half wave single-phase controlled rectifier with resistive load at  = 40°

A

AC AC

15 V 2 V

0-25 mA

470 Ω To CRO 1 μF

A G

K

The average voltage, V_dc , across the resistive load can be obtained by considering the waveform shown in Fig.1.

𝑉_𝑑𝑐 =_2𝜋¹ 𝑉_𝛼^𝜋 𝑚sin 𝜔𝑡 𝑑𝜔𝑡 =^𝑉_2𝜋^𝑚 −𝑐𝑜𝑠 𝜋 + 𝑐𝑜𝑠 𝛼 =^𝑉_2𝜋^𝑚 1 + 𝑐𝑜𝑠 𝛼 (1)

The maximum output voltage and can be achieved when  = 0 which is the same as diode case.

𝑉_𝑑𝑚 =^𝑉_𝜋^𝑚 (2)

The normalized output voltage is the DC voltage divided by maximum DC voltage, Vdm which can be obtained as shown in equation (3).

The rms value of the output voltage is shown in the following equation:-

𝑉_𝑟𝑚𝑠 = _2𝜋¹ 𝑉_𝛼^𝜋 𝑚sin 𝜔𝑡 ²𝑑𝜔𝑡= ^𝑉₂^{𝑚 1}_𝜋 𝜋 − 𝛼 +^{sin 2𝛼} ₂ (3)

Vn =Vdc /Vm = 0.5 (1+ cosα ) (4)

The rms value of the transformer secondary current and load is: 𝐼_𝑠 =^{𝑉𝑟𝑚𝑠}_𝑅 (5)

1. When triggered regularly(by providing gate current or voltage) and if sinusoidal voltages are applied to the SCR anode, it will turn off on each alternate half cycle i.e. when anode current decreases just below the holding current (I_H).By controlling the firing angle we can vary the average rectified current in each half cycle.

2. Control over a greater part of a cycle is possible with the introduction of a phase shifting RC network. The voltages across the capacitor will lag the applied voltages by an amount that depends upon the value of R or C. By varying the values of R or C different values of  may be obtained.

The phase shifting angle

𝛼 =2tan⁻¹(ωRC) ( in radians)

Where, C= 1 μF; R=0, 1 K, 2 K,…, 10 K & ω =2πf, where f = 50Hz

3. The anode current through the load resistance RL when SCR is conducting is given by, 𝐼_a = 𝑉_m

2π𝑅_L 1 + cos α

4. It can be seen that the load current increases abruptly at the point corresponding to the phase shifting angle 𝜙and then follows the sine variation until the supply voltages falls below VH at phase angle of (𝜙) and current remains zero until the phase shifting angle 𝜙 is reached again in the next cycle.

The average current i.e. the load current read by the ammeter:

𝐼_𝐿 =V_msin ωt − V_R R_L 𝐼_𝐷𝐶 = 1

2𝜋 𝐼_𝐿𝑑𝛼 = 1 2𝜋

V_msin ωt − V_R R_L

𝜋

𝜑 𝜋

𝜑

𝑑𝛼 I_DC =_2πR^Vm

L 1 + cos α

This relation shows that the average rectified current can be controlled by varying the angle of firing the SCR.

Procedure:

1. Make connections as shown in the circuit diagram.

2. Select 15 V AC and 2 V AC supply with the help of toggle switch.

3. Turn the decade resistance knob in the anti clock wise direction to its maximum value (R).

4. Now turn the power ON, SCR may not turn ON. Now reduce the value of R so that the SCR fires.

5. Record the anode current and find the angle  from the output waveform observed on CRO.

6. Repeat the above step choosing different values of resistances in decade resistance box.

7. Plot the phase firing characteristic of the SCR by plotting the phase shift () on X- axis and anode current on Y-axis.

Observations:

S. No Resistance (Ω)

Anode current in mA Phase shift 𝜙

Observed Value

(mA)

Calculated Value

𝐼_𝑎 = 𝑉𝑚

2𝜋𝑅_𝐿 1 + cos⁡(𝛼)

By CRO

𝛼 =360 × (𝑁𝑜. 𝑜𝑓 𝐷𝑖𝑣. ) 𝑇𝑖𝑚𝑒 𝑃𝑒𝑟𝑖𝑜𝑑 ×𝑡𝑖𝑚𝑒

𝐷𝑖𝑣

(degree)

Calculated

𝛼 = 2𝑡𝑎𝑛⁻¹ 𝜔𝑅𝐶

(degree)(keep calculator in degree mode)

Report:

1. What is the effect of varying R on the circuit performance in this experiment?

2. What is the function of the diode in the SCR gate circuit?

3. Draw the schematic symbols and applications of the following:

(a) Diac (b) Triac

4. What is meant by phase controlled rectifier?

5. Mention some of the applications of controlled rectifier.

Experiment No: 3 Object: To study the speed control of Universal motor using Traic.

Apparatus used:

S. No Lab No. Equipment Range/rating Qty. Make

Theory:

Fig. 1. Triac I-V Characteristics Curves

In Quadrant Ι, the triac is usually triggered into conduction by a positive gate current, labelled above as mode Ι+. But it can also be triggered by a negative gate current, mode Ι–. Similarly, in Quadrant ΙΙΙ, triggering with a negative gate current, –ΙG is also common, mode ΙΙΙ– along with mode ΙΙΙ+. Modes Ι–

and ΙΙΙ+ are, however, less sensitive configurations requiring a greater gate current to cause triggering than the more common triac triggering modes of Ι+ and ΙΙΙ–.

Also, just like silicon controlled rectifiers (SCR’s), triac’s also require a minimum holding current IH to maintain conduction at the waveforms cross over point. Then even though the two thyristors are combined into one single triac device, they still exhibit individual electrical characteristics such as different breakdown voltages, holding currents and trigger voltage levels exactly the same as we would expect from a single SCR device.

Triac Applications:

The Triac is most commonly used semiconductor device for switching and power control of AC systems as the triac can be switched “ON” by either a positive or negative Gate pulse, regardless of the polarity of the AC supply at that time. This makes the triac ideal to control a lamp or AC motor load with a very basic triac switching circuit of Fig. 2.

Procedure: -

1. Connections are made as shown in the circuit diagram.

2. Firing angle  is varied by changing the values of R & C in steps gradually.

3. Note down corresponding speed of the universal motor using Tachometer and tabulate.

4. A graph of  v/s speed is plotted.

Circuit Diagram:

Fig. 2.

Graph:

Fig. 3

Fig. 4 Waveforms for Triac firing circuit using a diac when (a) Pot. R is adjusted to minimum &

(b) Pot. R adjusted to maximum. (Reference: P. S. Bimbhra, Power Electronics, Khanna Publishers) A

AC

220 V 12 V

0-25 mA

To CRO 1 μF

MT1

G MT2

UM Rp

Snubber

Observations: C = 1 F (Constant)

S. No. Rp(Ohms) Firing angle ()in degrees (from CRO) Speed in RPM

Formula Used: tan (¹ ), ³⁹⁰⁰⁰⁰ 10000 390000

p p

CR R R

 ^   R^ 

 Result:

Speed control of Universal Motor is studied and a graph of  v/s speed is plotted Report:

1. What are the different methods to turn on the thyristor?

2. How can a thyristor turned off?

3. What is a snubber circuit?

4. What losses occur in a thyristor during working conditions?

5. Define hard-driving or over-driving.

6. Define circuit turn off time.

7. Why circuit turn off time should be greater than the thyristor turn-off time?

8. What is the function of freewheeling diodes in controlled rectifier?

9. What are the advantages of freewheeling diode in a controlled rectifier?

10. What is meant by delay angle?

11. Plot graph of  v/s speed and comment on the graph.

Experiment No: 4 Object:

a) To determine experimentally the transfer function of the given lead compensating network.

b) Obtain its frequency response for its magnitude (dB) and phase (degrees).

c) To verify the same using the theoretical analysis.

APPARATUS REQUIRED: -

S. No. Name of the Apparatus Range or Values Quantity 1. Resistors and capacitors

2. Bread Board 3. Signal Generator 4. C.R.O. with probes 5. Connecting wires THEORY: -

FORMULAE USED: -

1. The transfer function of a lead compensator is given by, 𝐺 𝑠 =^{𝛼 1+𝑠𝜏} _{1+𝑠𝛼𝜏} 𝑤𝑕𝑒𝑟𝑒 𝛼 < 1 2. Constant factor = _𝑅^𝑅2

1+𝑅2 , which is always less than unity.

3. Also, the constant factor 𝛼 = ^{1−𝑠𝑖𝑛 𝜙}_{1+𝑠𝑖𝑛 𝜙}^𝑚

𝑚 where m is the maximum phase angle lead in deg.

4. The maximum frequency at which maximum phase lead occurs, is, ωm = 2πf rad/sec. where, f is the maximum frequency in Hz at which maximum phase lead occurs.

5. The maximum frequency at which maximum phase lead occurs is, 𝜔_𝑚 = ¹

𝛼∗𝜏 rad/sec 6. The time constant



7. Phase angle 𝜙° = sin^{−1 𝑌}_𝑌¹

2 for the lissajous fig (a) shown below.

8. Phase angle 𝜙° = 180 − sin^{−1 𝑌}_𝑌¹

2 deg for the lissajous fig (b) shown below.

PROCEDURE: -

1. Connections are made as per the circuit diagram.

2. The output voltage of sine generator is set to 10 V (peak to peak) and is supplied as input to the RC lead compensator.

3. A CRO is connected at the output of the lead compensator.

4. The input frequency of the circuit is varied in steps and the corresponding phase angle is calculated using Lissajous figure in CRO.

5. The voltage gain is calculated using the formula as given in the table.

6. The plots of gain in dB Vs frequency and phase angle Vs frequency are plotted in semi log sheet.

7. The plot of phase angle Vs frequency is plotted in semi log sheet.

8. From this plot, the maximum phase lead m in degrees and the frequency at which this maximum phase lead occurs f in Hz are found.

9. With these values and using the above formulae, the transfer function of the given RC phase lead compensating network is found.

TABULAR COLUMN: - Input voltage V_i = ____volts (Peak-Peak) S. No. Frequency

(Hz)

Output Voltage V_o (PP) volts

Gain in dB =

20*log(V_o/V_i) Y1 Y2

Phase angle

(degrees)

SAMPLE CALCULATIONS: -

...

...

DETERMINATION OF TRANSFER FUNCTION: -

Step 1: From the plot of phase angle vs frequency, obtain the maximum phase lead



Step 2: Using the formula, ωm = 2πf, compute the maximum frequency in rad/sec.

Step 3: Using the formula, = ^{1−𝑠𝑖𝑛 𝜙}_{1+𝑠𝑖𝑛 𝜙}^𝑚

𝑚 , compute the constant factor α in the transfer function.

Step 4: Using the formula, 𝜏 = _𝜔 ¹

𝑚∗ 𝛼 compute the time constant τ in sec.

Step 5: Using the formula, 𝐺 𝑠 = ^{𝛼 1+𝑠𝜏} _{1+𝑠𝛼𝜏} 𝑤𝑕𝑒𝑟𝑒 𝛼 < 1, write the transfer function.

Step 6: Verify the same, as follows.

VERIFICATION: -

Step 1: From the given RC phase lead compensator network, collect the values of the components R₁, R₂ and C.

Step 2: With the help of the formula, 𝛼 = _𝑅^𝑅2

1+𝑅2 obtain the value of constant factor α in the transfer function.

Step 3: With the help of the formula,  = R1C, obtain the value of time constant in sec.

Step 4: Using the formula, 𝐺 𝑠 = ^{𝛼 1+𝑠𝜏} _{1+𝑠𝛼𝜏} 𝑤𝑕𝑒𝑟𝑒 𝛼 < 1 write the transfer function.

RESULT: -

Thus, the transfer function of the given lead compensating network is verified experimentally Report: 1. What are the effects of phase lead compensation?

2. Write advantages and disadvantages of phase lead compensation.

-20 -15 -10 -5 0

Magnitude (dB)

100 1,000 3,316.6 11,000 100,000 1,000,000

-56.443 -30 0

Phase (deg)

Bode Diagram( =(1/11);  =1 ms)

Frequency (rad/s)

m

1/

1/*

m=1/(*)

Experiment No: 5 Object:

a) To determine experimentally the transfer function of the given lag compensating network.

b) Obtain its frequency response for its magnitude (dB) and phase (degrees).

c) To verify the same using the theoretical analysis.

APPARATUS REQUIRED: -

S. No. Name of the Apparatus Range or Values Quantity 1. Resistors and capacitors

2. Bread Board 3. Signal Generator 4. C.R.O. with probes 5 Connecting wires THEORY: -

FORMULAE USED: -

1. The transfer function of a lag compensator is given by, 𝐺 𝑠 = _{1+𝑠𝛽𝜏} ^1+𝑠𝜏 𝛽 > 1 2. Constant factor = ^𝑅1_𝑅^+𝑅2

2 , which is always greater than unity.

3. Also, the constant factor 𝛽 = ^{1+𝑠𝑖𝑛 𝜙}_{1−𝑠𝑖𝑛 𝜙}^𝑚

𝑚 where _m is the maximum phase angle lag in deg.

4. The maximum frequency at which maximum phase lag occurs, is, ω_m = 2πf rad/sec. where, f is the maximum frequency in Hz at which maximum phase lag occurs.

5. The maximum frequency at which maximum phase lag occurs is, 𝜔_𝑚 = _𝛽∗𝜏¹ rad/sec 6. The time constant  = R2C sec.

7. Phase angle 𝜙° = sin^{−1 𝑌}_𝑌¹

2 for the lissajous fig (a) shown below.

8. Phase angle 𝜙° = 180 − sin^{−1 𝑌}_𝑌¹

2 for the lissajous fig (b) shown below.

PROCEDURE: -

1. Connections are made as per the circuit diagram.

2. The output voltage of sine generator is set to 10 V (peak to peak) and is supplied as input to the RC lag compensator.

3. A CRO is connected at the output of the lag compensator.

4. The input frequency of the circuit is varied in steps and the corresponding phase angle is calculated using Lissajous figure in CRO.

5. The voltage gain is calculated using the formula as given in the table.

6. The plots of gain in dB vs frequency and phase angle vs frequency are plotted in semi log sheet.

7. The plot of phase angle vs frequency is plotted in semi log sheet.

8. From this plot, the maximum phase lag m in degrees and the frequency at which this maximum phase lag occurs f in Hz are found.

9. With these values and using the above formulae, the transfer function of the given RC phase lag compensating network is found.

TABULAR COLUMN: - Input voltage V_i = ____volts (Peak-Peak) S. No. Frequency

(Hz)

Output Voltage Vo (PP) volts

Gain in dB = 20*log(Vo/Vi)

Y1 Y2 Phase angle  (degrees)

SAMPLE CALCULATIONS: -

...

...

DETERMINATION OF TRANSFER FUNCTION: -

Step 1: From the plot of phase angle Vs frequency, obtain the maximum phase lag m in degrees and the frequency at which this maximum phase lag occurs f in Hz

Step 2: Using the formula, ωm = 2π f , compute the maximum frequency in rad/sec.

Step 3: Using the formula, 𝛽 = ^{1+𝑠𝑖𝑛 𝜙}_{1−𝑠𝑖𝑛 𝜙}^𝑚

𝑚 , compute the constant factor  in the transfer function.

Step 4: Using the formula, 𝜏 = ¹

𝜔𝑚∗ 𝛽 compute the time constant τ in sec.

Step 5: Using the formula, 𝐺 𝑠 = _{1+𝑠𝛽𝜏} ^1+𝑠𝜏 , 𝛽 > 1,, write the transfer function.

Step 6: Verify the same, as follows.

VERIFICATION: -

Step 1: From the given RC phase lag compensator network, collect the values of the components R1, R2 & C.

Step 2: With the help of the formula, 𝛽 = ^𝑅1_𝑅^+𝑅2

2 , obtain the value of constant factor  in the transfer function.

Step 3: With the help of the formula,  = R2C , obtain the value of time constant  in sec.

Step 4: Using the formula, 𝐺 𝑠 = _{1+𝑠𝛽𝜏} ^1+𝑠𝜏 , 𝛽 > 1, write the transfer function.

RESULT: -

Thus, the transfer function of the given lag compensating network is verified experimentally.

Report: 1. What are the effects of phase lag compensation?

2. Write advantages and disadvantages of phase lead compensation.

-20.6 -15 -10 -5 0

Magnitude (dB)

10⁰ 10¹ 10² 10³ 10⁴ 10⁵

0 30 56.443

Phase (deg)

Bode Diagram ( = 1 ms;  = 11; C = 0.1 F)

Frequency (rad/s)

m=56.443^ 1/=10000

1/(*)=90.9

m=1/(*)=301.51

Experiment No: 6 (a)

Object: To study and observe different wave-shapes on Op-Amp based Differentiator.

Apparatus Used:

S.No. Lab No Equipment Rating/Range Make

Theory of Differentiator: Operational amplifier is a direct coupled high gain differential amplifier with high input impedance and low output impedance. It is used to perform various arithmetical operations such as addition, subtraction, integration, differentiation and hence the name is Operation Amplifier

The pin configuration of 741- Op-Amp are given below

Specifications Applications Features

 Supply Voltage ± 18V

 Internal Power Dissipation 310 mw

 Differential input voltage

± 30V

 Input Voltage ± 15V

 Operating temperature range 0ºC to 70ºC

 Non-inverting amplifier

 Inverting amplifier

 Integrator

 Differentiator

 Low Pass,

 High Pass,

 Band pass and

 Band Reject Filters

 No External frequency compensation is required

 Short circuit Protection

 Off Set Null Capability

 Large Common mode and differential Voltage ranges

 Low Power Dissipation

 No-Latch up Problem

 741 is available in three packages: 8-pin metal can, 10-pin flat pack and 8 or 14-pin DIP

As the name suggests, the circuit performs the mathematical operation of differentiation, i.e. the output voltage is the derivative of the input voltage.

𝑽_𝒐 = −𝑹_𝒇𝑪_𝟏𝒅𝑽_𝒊𝒏 𝒅𝒕

Both the stability and the high-frequency noise problems can be corrected by the addition of two components: R1 and Cf, as shown in the circuit diagram. This circuit is a practical differentiator. The input signal will be differentiated properly if the time period T of the input signal is larger than or equal to R_fC₁. That is, T ≥ R_fC₁ Differentiator can be designed by implementing the following steps.

1. Select fa equal to the highest frequency of the input signal to be differentiated. Then, assuming a value of C1<1 μF, calculate the value of Rf

2. Calculate the values of R₁and C_f so that R₁C₁=R_fC_f. Differentiator has wide applications in:

1. Monostable Multivibrator 2. Signal wave shaping 3. Function Generators.

Circuit Diagram:

Rf = 15 kΩ

Cf = 470 pF R1 = 820 Ω

Rcomp = 820 Ω RL = 10 kΩ

Vin

Vout

+12V

-12V 2

3 7 4 C1 = 0.01μF 6

Adding the input resistor Rin limits the differentiators increase in gain at a ratio of Rƒ/Rin. The circuit now acts like a differentiator amplifier at low frequencies and an amplifier with resistive feedback at high frequencies giving much better noise rejection. Additional attenuation of higher frequencies is accomplished by connecting a capacitor Cƒ in parallel with the differentiator feedback resistor, Rƒ. This then forms the basis of an Active High Pass Filter.

Simple Differentiator Circuit

Improved Differentiator Circuit

Procedure:

1. Do the proper biasing of Op-Amp by connecting +Vcc on pin no. 7 and −Vcc on pin no. 4. (Vcc = 12V).

2. Test the Op-Amp in Unity Gain.

3. Make the circuit on Bread board

4. Choose the value of R and C such that the time period of input signal Vi is much higher than RC time constant. ( Take T = 10RC)

5. Apply sine wave at the input terminals of the circuit using function Generator.

6. Connect channel-1 of CRO at the input terminals and channel-2 at the output terminals.

7. Observe the output of the circuit on the CRO which is a cosine wave (90o phase shifted from the sine wave input) and note down the position, the amplitude and the time period of V_in & V_o.

8. Now apply the square wave as input signal.

9. Observe the output of the circuit on the CRO which is a spike wave and note down the position, the amplitude and the time period of V_in & V_o.

10. Plot the output voltages corresponding to sine and square wave inputs.

Observation:

Trace the output waveform for different input waves (square, Sinusoidal) and note down the Amplitude and time period for every waveform.

Sl.

No.

Input Signal

Time Period (second)

Input Voltage (Vin)

Output Voltage (Vo)

Phase Shift (degrees) Sine

Squire Triangular Result:

EXPECTED WAVEFORMS:

Report and Comments:

1. What is the symbol of op-amp?

2. Draw the pin diagram of op-amp.

3. What is the supply voltage range that an op-amp can with stand?

4. What is the input voltage range that an op-amp can with stand?

5. What are the available package types of IC741?

6. What is a virtual ground? What are the differences between the physical ground and the virtual ground?

7. What is the current flowing through the input terminals of an Ideal op-amp?

8. Which loop voltage gain is larger, closed or open?

9. What is the normal value of saturation voltage of an op-amp?

10. Mention a few applications of op-amp.

11. Mention some features of op-amp.

12. What is a Differentiator?

13. Draw the circuit of the Differentiator using op-amp IC741.

14. Write down the expression for Vo of a Differentiator.

15. Draw the output waveform of the Differentiator when the input is a Sine wave.

16. Why R1 and Cf are connected in the circuit of the Differentiator?

17. What are the applications of Differentiator?

18. Why Rcomp is used in both Integrator and Differentiator circuits?

Experiment No: 6 (b)

Object: To study and observe different wave-shapes on Op-Amp based Integrator.

Apparatus Used:

S.No. Lab No Equipment Rating/Range Make

THEORY: Integrator: Operational amplifier is a direct coupled high gain differential amplifier with high input impedance and low output impedance. It is used to perform various arithmetical operations such as addition, subtraction, integration, differentiation and hence the name is Operation Amplifier.

The pin configuration of 741- Op-Amp are given below

Specifications Applications Features

 Supply Voltage ± 18V

 Internal Power Dissipation 310 mw

 Differential input voltage

± 30V

 Input Voltage ± 15V

 Operating temperature range 0ºC to 70ºC

 Non-inverting amplifier

 Inverting amplifier

 Integrator

 Differentiator

 Low Pass,

 High Pass,

 Band pass and

 Band Reject Filters

 No External frequency compensation is required

 Short circuit Protection

 Off Set Null Capability

 Large Common mode and differential Voltage ranges

 Low Power Dissipation

 No-Latch up Problem

 741 is available in three packages: 8-pin metal can, 10-pin flat pack and 8 or 14-pin DIP

A circuit in which the output voltage is the integration of the input voltage is called an integrator.

𝑽_𝒐 = − 𝟏

𝑹_𝟏𝑪_𝒇 𝑽_𝒊𝒏𝒅𝒕

In the practical integrator circuit to reduce the error voltage at the output, a resistor Rf is connected across the feedback capacitor C_f. Thus, R_f limits the low-frequency gain and hence minimizes the variations in the output voltage.

The frequency response of the integrator is shown in the Fig. 2. fb is the frequency at which the gain is 0 dB and is given by

𝒇_𝒃= − 𝟏 𝟐𝝅𝑹_𝟏𝑪_𝒇

In this figure there is some relative operating frequency, and for frequencies from f to fa the gain ^𝑅_𝑅^𝑓

1 is constant. However, after f_a the gain decreases at a rate of 20 dB/decade.

In other words, between f_a and f_b of Fig. 2, the circuit acts as an integrator. The gain limiting frequency 'fa' is given by

𝒇_𝒂 = 𝟏 𝟐𝝅𝑹_𝒇𝑪_𝒇 Circuit Diagram:

Rf = 15 kΩ

C_f = 0.01μF R1 = 1.5 kΩ

R_comp = 1.5 kΩ R_L = 10 kΩ

Vin

V_out +12V

-12V 2

3 7 4

6

Fig. 1. Circuit Diagram

Normally it is f_a<f_b. From the above equation, we can calculate R_f by assuming f_a & C_f. This is very important frequency. It tells us where the useful integration range starts.

If fin < fa - circuit acts like a simple inverting amplifier and no integration results, If fin = fa - integration takes place with only 50% accuracy results,

If f_in = 10f_a - integration takes place with 99% accuracy results.

In the circuit diagram of Integrator, the values are as: C_f=0.01μF; R_f=15 kΩ. ∴ fa =1061 Hz. Hence the input frequency is to be taken as 10610 Hz to get 99% accuracy results.

Integrator has wide applications in:

1. Analog computers used for solving differential equations in simulation arrangements.

2. A/D Converters.

3. Signal wave shaping.

4. Function Generators.

Fig. 2. Frequency Response of Integrator

Procedure:

1. Do the proper biasing of Op-Amp by connecting +V_cc on pin no. 7 and −V_cc on pin no. 4. (V_cc = 12 V).

2. Test the Op-Amp in Unity Gain.

3. Make the circuit on Bread board.

4. Choose the value of Rf and Cf such that the time period of input signal Vi is much smaller than RfCf time constant. ( Take T = R_fC_f /10)

5. Apply sine wave at the input terminals of the circuit using function Generator.

6. Connect channel-1 of CRO at the input terminals and channel-2 at the output terminals.

7. Observe the output of the circuit on the CRO which is a cosine wave (90° phase shifted from the sine wave input) and note down the position, the amplitude and the time period of Vin & Vo.

8. Now apply the square wave as input signal.

9. Observe the output of the circuit on the CRO which is a triangular wave and note down the position, the amplitude and the time period of V_in & V_o.

10. Plot the output voltages corresponding to sine and square wave inputs.

Observation:

Trace the output waveform for different input waves (square, Sinusoidal) and note down the Amplitude and time period for every waveform.

S.

No.

Input Signal

Time Period (second)

Input Voltage (Vin)

Output Voltage (Vo)

Phase Shift (degrees) Sine

Square Triangular

EXPECTED WAVEFORMS:

Result:

...

Report and Comments:

1. What is the supply voltage range that an op-amp can with stand?

2. What is the input voltage range that an op-amp can with stand?

3. What are the available package types of IC741?

4. What is a virtual ground? What are the differences between the physical ground and the virtual ground?

5. What is the current flowing through the input terminals of an Ideal op-amp?

6. Which loop voltage gain is larger, closed or open?

7. What is the normal value of saturation voltage of an op-amp?

8. Mention a few applications of op-amp.

9. Mention some features of op-amp.

10. What is an Integrator?

11. Draw the frequency response of the Integrator and explain.

12. Draw the output waveform of the Integrator when the input is a Square wave.

13. What is the purpose behind the connection of Rf in the feedback path of Integrator?

14. What are the applications of Integrator?

15. Why Rcomp is used in both Integrator and Differentiator circuits?

Experiment No. 7

OBJECT:-To study the Time Response of a Second Order series RLC System to determine the parameters of L & C from unit step input.

APPARATUS:-

S. No. Name of Apparatus Specifications Make 1. Second Order System study unit.

2. CRO 3. Multimeter CIRCUIT DIAGRAM:-

THEORY:-

The transfer function which relates input voltage and capacitor voltage is 𝑉_𝐶 𝑠

𝑉_𝑖 𝑠 = 1

𝐿𝐶𝑠²+ 𝑅𝐶𝑠 + 1 The characteristic equation is

𝐿𝐶𝑠²+ 𝑅𝐶𝑠 + 1 = 0 or 𝑠²+^𝑅_𝐿𝑠 +_𝐿𝐶¹ = 0

By comparing with a standard characteristic equation 𝑠²+ 2𝛿𝜔_𝑛𝑠 + 𝜔_𝑛² = 0 we get, 𝛿 =^𝑅₂ ^𝐶_𝐿 and 𝜔_𝑛 = ¹

𝐿𝐶 where δ = Damping Ratio, and n = Undamped natural frequency PROCEDURE:-

1. Make the connections are per the circuit diagram.

2. Adjust the input square wave such that the magnitude of the wave is 1 V (p-p). (Check the square wave in CRO by placing CRO in Channel 1 mode).

3. Observe the time response (V_C) on the CRO (Channel 2) by selecting different values of resistances by changing the knob provided on the decade resistor.

4. Set the resistance to a fixed value. Use multimeter to measure the resistance and take the corresponding values of Peak Time (𝑇_𝑃) i.e. 𝑇_𝑃 =_𝜔 ^𝜋

𝑛 1−𝛿² , Peak Over Shoot (𝜇_𝑃) (i.e. Max Peak Value -1) or 𝜇_𝑃 = 𝑒⁻

𝛿𝜋

1−𝛿2 using trace papers.

5. Calculate Damping Ratio (δ), Undamped Natural Frequency (ω_n) from the following formulae 𝛿 = ^{𝑙𝑛 𝜇𝑃}

2

𝜋²+ 𝑙𝑛 𝜇_𝑃 ² and 𝜔_𝑛 =_𝑇 ^𝜋

𝑝 1−𝛿2

6. Calculate the parameters L & C of RLC system using the following formulae 𝛿 =^𝑅₂ ^𝐶_𝐿 and 𝜔_𝑛 = _𝐿𝐶¹

7. Now calculate Settling Time (TS), and Damped Frequency (^d) using the following formulae 𝑇_𝑠 =_𝛿𝜔⁴

𝑛 (2% 𝑆𝑒𝑡𝑡𝑙𝑖𝑛𝑔 𝑡𝑖𝑚𝑒) and 𝜔_𝑑 = 𝜔_𝑛 1 − 𝛿²

8. Repeat Step 4 to 7 for different values of Resistances and tabulate the readings.

9. Find out average L & C values.

R L

Channel-1 C Channel-2

Observation Table:-

Sl.

No.

Resistance in Ω

Maximum Peak Overshoot (μP) in V

Peak Time (TP) in ms

Damping Ratio

𝛿 = 𝑙𝑛 𝜇_𝑃 ² 𝜋²+ 𝑙𝑛 𝜇_𝑃 ²

Undamped natural frequency in rad/s 𝜔𝑛=_𝑇 ^𝜋

𝑝 1−𝛿2

Damped frequency (𝜔𝑑) in rad/s 𝜔_𝑑= 𝜔𝑛 1 − 𝛿²

Settling Time (TS) in ms

𝑇𝑠

= 4 𝛿𝜔𝑛

C = 2𝛿 𝑅𝜔𝑛

(F) L = 𝑅 2𝛿𝜔𝑛

(H)

MODEL GRAPH:-

RESULT :-

1. Studied the Time Response of a Second Order series RLC System and determined the parameters of L, C and verified the Settling Time (TS) from unit step input.

2. For R=...Ω, Obtained values of L= & C=

3. For R=... Ω, Obtained values of L= &C=

Report:

1. Compare results with theoretical values of the parameters.

2. Define: (a). Delay Time, (b). Rise Time, (c). Peak Time, (d). Settling time, (e). Maximum Overshoot, (f). Steady state error.

3. Calculate Rise Time from 𝑇_𝑟 =^{𝜋−𝑡𝑎𝑛}

−1 1−𝛿2 𝛿 𝜔_𝑛 1−𝛿²