Rectifiers

Rectifiers
Rectifier converts AC into DC.
We need DC voltages to run many of our appliances at home such as television, radio, computer etc.
Only lamps, fans etc can work on AC power directly. Therefore; we need to convert the AC main’s power received at our homes into DC in each of these gadgets to run them. Furthermore; it is only AC which can be stepped up and stepped down so easily. We can use a semi conductor on pn junction diode and convert AC into DC.

Types of Rectifier

Half Wave Rectifier
The half wave rectifier is made up of a diode and a resistor as shown in the fig. The half wave rectifier is used to eliminate either positive or negative part of the input.

Figure: Positive half wave rectifier

Negative Half Wave Rectifiers
Fig. shows a half wave rectifier with diode direction is reversed. In this circuit the diode will conduct on the negative half cycle of the input, and
                                                            VL = V2.
The diode will be reversed biases for the positive half cycle of the input and
                                                            VD = V2.
As a result positive half cycle of the input is eliminating. The operating principle of the negative half wave rectifier is same as the positive half wave rectifiers. The only difference is the polarity of the output will be reversed.

Figure: Negative Half wave rectifier 

Full Wave Rectifiers
The full wave rectifier consists of two diodes and a resistor, as shown in the fig (a).

Figure: Positive full wave rectifiers

The result of this change in circuit is illustrated in fig (b).
In the fig (b), the output from the full wave rectifier is compared with that of a half wave rectifier.

Negative Full wave Rectifiers
The main differences between the positive and negative full wave rectifier are the direction that the diodes are pointing and the polarity of the output voltage.
The analysis of the negative full wave rectifier circuit is same as negative half wave rectifier.
If we reverse the direction of the diodes in the positive full wave rectifier, we will have a negative full wave rectifier as shown in the fig.

Figure: Negative full wave rectifier

Full Wave Bridge rectifier
The bridge rectifier is the most commonly used full wave rectifier circuit for several reasons
(1) It does not require the use of center-tapped transformer, and therefore can be coupled directly to the ac power line, if desired.
(2)Using a transformer with the same secondary voltage produces a peak output voltage that is nearly double the voltage of the full wave center-tapped rectifier. This results in the higher dc voltage from the supply.

Figure: Bridge full wave rectifier

My Laboratory Experiment
I have created all the three rectifiers on a single board. It was a real fun for me. May be when I show the circuits; you people will not recognize that which circuit belong to a type of rectifier.  I connected a 6V transformer to each of the rectifier and then observe their output on oscilloscope. The output produced was according to its operation.

Figure: All the three rectifiers on single board

Thevenin’s Theorem

Thevenin’s Theorem
The Thevenin’s theorem is a useful theorem by which a complex circuit can be reduced to an equivalent series circuit consisting of a single voltage source (V_th) and a series resistance (R_th) and a load resistance (R_L).
After creating the thevenin’s equivalent circuit, we may then easily determine the load voltage (V_L) and the load current (I_L).

Figure: Thevenin’s equivalent circuit

Example
Find the thevenin’s voltage; thevenin’s equivalent resistance and then voltage across the load in the given circuit.

Figure: Example circuit

Thevenin’s Voltage
Remove the load at terminal A and B. Now no current will be flowing via R3. With no current via R3, there is no voltage drop across R3. Therefore; V_{th =} V_{R2 .}

Figure: Circuit for thevenin’s voltage

This is the thevenin’s equivalent voltage.

Thevenin’s Resistance
Remove all the source voltages and replace them with a short while retaining any internal resistance. Remove all the current sources and replace them with an open while retaining any internal source resistance.

Figure: Circuit for thevenin’s resistance

The equation for R_th is;

R_{th  =}  R3 + R1 * R2 / R1 + R2

Load Voltage
The below figure shows thevenin’s equivalent circuit;

Figure: Thevenin’s equivalent circuit

The equation for voltage across load is;
V_L = V_th * R_L / R_th + R_L

Experiment
Below is the circuit for my experiment of thevenin’s theorem;

Figure: Circuit for thevenin’s theorem verification

I connect a 10V voltage source to the circuit. I then remove the load resistance from the circuit and calculate the thevenin’s voltage which is around 6.02 V
I then removed the voltage source from the circuit and made it short circuit and calculate the thevenin’s resistance which is 7.19 (ohms).
Now I again connected a voltage source and load resistance and measure a voltage against load resistance using volt meter which is around 2.13 V.
I have calculated a thevenin’s voltage and resistance. Therefore;  I then used a potentiometer for adjustment of thevenin’s resistance which is 7.19 ohms and thevenin’s voltage 6.02 using voltage source and measure the voltage across load which is around 2V; approximately equal to voltage across the load when connect complex circuit.
Hence; Thevenin’s theorem is verified.

Kirchoff’s Law

Kirchoff’s Voltage Law
At any instant; the sum of all the voltage sources in any closed circuit is equal to the sum of the entire voltage drop in that circuit.
Sum of all the voltage sources = sum of all the voltage drop in a circuit
In other words, at any instant the algebraic sum of all the voltages around any closed circuit is zero.
Sum of all the voltage sources – sum of all the voltage drop in a circuit = 0

In the circuit shown; the voltage across the resistor using ohms law are IR1, IR2 and IR3.

Figure: Example for KVL

The (+) ive and (-)ive for V is different from those for the resistors. The (+) ive is shown at a higher voltage.

V = IR1 + IR2 + IR3
V – IR1 – IR2 – IR3 = 0

Consider the 2^nd circuit;

Figure: Example for KVL

My Laboratory Experiment

Figure: My Circuit for KVL

I have connected a 6V DC voltage source to my circuit to verify the KVL. First I have calculated the voltage of voltage source connected in the circuit via volt meter and I got 6V reading on voltmeter.
I then measure the voltage across each of the resistor and then summed up and find that voltages across all resistors are equal to voltage source connected.
R1= 220 Ohms = 2.27V
R2 = 120 0hms = 2.24 V
R3 = 100 ohms = 1V

So the total voltage drop across all the resistors is approximately 6V.

Why I got approximated voltage drop for resistors?
The reason is because of resistors tolerance value.

My Lab Equipment

Bread Board
Bread board is used for construction of various circuits for testing. This is very useful since here; we don’t have to solder the different components.

Figure: Bread board for circuit preparation

Digital Multi meter
A multi meter is indeed a multi meter. It can measure dc and ac voltage, current and in addition resistance.
In some recent multi meters we can measure even frequency and capacitance.

Figure: Digital multi meter (DMM)

Testing the bread board
We can do that by using a digital multi meter (DMM) and a couple of wires. Insert the wire in to two holes between which you want to check the electrical continuity.
Use the DMM in resistance mode and connect the two probes of the DMM to the two strips of wires.
If the resistance shown is zero then they are connected. If the DMM reads high resistance then the two points are dis-connected electrically.

Figure: Testing the bread board for connectivity (zero resistance)

Power Supply
For performing experiments, we need a power supply which can provide the necessary power to activate the circuits. The power supply, we will be using here as the following outputs;
0 to 30 V variable DC voltages, 1A (max)
The voltage can be read on digital display panel.

-15_0_15  (Dual Supply, 1.5A (Max).
5V fixed DC voltage, 3A max.

Figure: Regulated power supply

First Integrated Circuit

First Integrated Circuit(IC)
Jack Killby of the Taxas Instrumentation and Robert Noyace of Fairchild Semiconductors are the inventors of integrated circuits.
Integrated circuits can be found in almost every modern electrical device such as computers, cars, television set, CD players, And Cellular phones etc.
Use semiconductor not just for transistor and diodes but also for resistors and capacitors, putting every thing on the same substrate.
The bulk resistively of the semiconductor and its diffusion doped layers could be exploited for fabrication resistors; p-n junctions could provide capacitance.

First Integrated Circuit

Figure: First Integrated Circuit

Modern Integrated Circuit

Figure: Modern Integrated Circuit (IC)