BPH 221 Lecture Series: Lecture 4 (Diode Rectification)

Direct Current (DC):  It is characterised by a uniform direction of flow and a steady Voltage level (amount) with respect to time.

Figure 4.1: Shows direct current with Amplitude of Voltage with respect to time.

Shown in the figure 4.1 is the direction of DC current with its voltage amplitude sketched with respect to time. We can observe that the voltage level is steady at any given time with a direct current flow.  We can recall that current just a the movement of electrons through a conductor, in DC, the electrons flow steadily in a single direction (forward).

Alternating Current (AC): On the contrary, AC is an electric current that reverses its direction many at regular intervals with respect to time. The flow of charges (i.e. electrons) periodically reverses direction. Also its voltage level (amplitude)  fluctuates from Peak positive (+V_p) to zero to peak negative (-V_p). 

 






              (a)                                (b)                              (c)

Figure 4.2:  AC Sine Waveform.

Figure 4.2 (a) is an example of a typical sine waveform of an AC, 4.2(b) depicts how the current in the AC changes direction with respect to time, while figure 4.2(c) illustrates how the voltage amplitude changes from +V_p to -V_p.

For an AC voltage;

            V_in= Vp Sin (ωt)

             V_in is the  input voltage

             V_p  is the peak voltage

            ω  =  2πf

The DC component of the signal V_dc = V_av  = 0

(Since we have equal voltage amplitude pulses in the positive and negative portion of the wave). 

But the root-mean-square voltage can be given by;

This is equal to the DC Voltage that delivers the same average power to a resistor as the periodic Voltage of an AC.

Recently, most electronics appliances we have today are comprises of semiconductor devices (e.g. diodes, transistors, Field Effect Transistors (FETs), e.t.c) which a preferred direction for current flow (DC) but, alternating current (AC) is supplied in the mains of our homes because it is easier to transmit over a long distance and redistribute. These necessitate a means of converting the supplied AC to DC in most of these devices for them to work appropriately. The process of converting AC to DC is known as rectification and it is achieved in electronics with an appropriate use of a diode.

The most common application of a rectifier is in the design of a circuit, which is a gateway into most electronics devices and equipment called power supply. In the power supply we employ the transformer to bring the AC electricity component (i.e. Voltage or current) to the required level either increase (step-up) or reduce (step down), before  it is rectified to produce the expected DC output. I will briefly discuss the basic working principle of a transformer here; before I delve into discussion about the rectifiers and at the end we would have explored the components that make up a power supply in an electronics device.

The Transformer

A transformer is a very common magnetic structure found in many applications. It is used to connect AC circuits to each other. It couples two circuits together magnetically rather than through any direct connection. Its main use is to raise or lower voltage and current between one circuit and the other.

A transformer is a necessary component in all power supply; it is applied in small power supply circuit for example in you small devices like in figure 4.3, it also find application in Electrical power system transmission and distribution, as shown in figure 4.4.

 

Figure 4.3: Transformer in small power supply

Figure 4.4:  Transformer application in electrical power transmission and distribution

An Ideal Transformer consists of two conducting coils wound on a common core, made of high grade iron with no electrical connection between the coils; they are connected to each other through magnetic flux.

The arrangement of primary and secondary windings on the transformer core is shown in figure 4.5 below. The voltage, current and flux due to the current in the primary winding is also shown.

Figure 4.5

The voltage relationship in a transformer is given by;

           V₁  -  is the voltage across the primary winding of the transformer

            V₂ – is the voltage output from the secondary winding of the transformer

            N₁  - is the number of turns in the primary winding

            N₂ – is the number of turns in the secondary winding

            a  =  is the ratio of N₁:N₂

This ration a, determines the amount of voltage change form the primary to the secondary winding of the transformer.

The current relationship of an Ideal transformer is given by the equation;

In summary, an Ideal transformer divides a sinusoidal input voltage by a factor of a and multiplies a sinusoidal current by a to obtain secondary voltage and current.

The voltage and current are expressed in terms of their RMS values.

The equivalent circuit of an ideal transformer can be drawn as follows

 

Figure 4.6: Equivalent Circuit of an Ideal Transformer

If a <1, i.e. N1<N2

The output voltage is greater than the input voltage and the transformer is called a step-up transformer

If a>1, i.e. N1>N2;

The output voltage is smaller than the input voltage and the transformer is called a step-down transformer.

If a =1, i.e. N1=N2;

The output voltage is the same as the input voltage and the transformer is called an isolation transformer. This is applied in a very useful application where two circuits need to be electrically isolated from each other.

      (a)                                 (b)                         (c)

Figure 4.7: a: Step-up transformer, b: Step-down transformer, c: Isolation transformer

There are some application in which the secondary winding is tapped at two different points, giving rise to two output circuits, for example in center-tapped transformer which splits the secondary voltage into two equal voltages as in figure 4.8.

Figure 4.8: Center-tapped transformer

Sample Question:

A transformer is required to deliver 1A current at 12V from a 220V rms Supply voltage. The number of turns in the primary is 2000.

i.  How many turns are required in the secondary winding?

ii.  What is the current in the primary winding?

Half Wave Rectifier

Now, we’ve come to the most popular application of diodes. Rectification can be simply defined as the conversion of alternating current (AC) to direct current DC). The simplest kind of rectifier is the half wave rectifier. In this, only one half of an AC waveform is allowed to pass through the load. We are familiar with the fact that a diode only allow current to flow when it is forward biased, if we forward bias a diode with an AC, considering the waveform in figure 4.9 (a), when the AC voltage is in the portion in blue color the polarity is reversed and the diode connection is reversed i.e. reversed bias. At this time there is no current flow and the voltage amplitude will be zero since V=IR, in the output we can see only the black colored potion of the waveform. If the diode is reversed in the connection as in figure 4.9(b), only the blue portion of the waveform will be passed for the same reason as in figure 4.9(a)

Figure 4.9: Half wave rectifier

With the Half wave rectifier, we have;

Sample Question 2:

Assume a 40:1 transformer with a 240V r.m.s input of 50Hz, determine the peak voltage, the dc voltage and the voltage at the load.

Let's Go To the Virtual Laboratory and demonstrate Half-Wave Rectifier:

Lab 1
In the Lab 1, we can see the circuit contains a function generator used to generate AC of 220V, 6Hz sent as input to a transformer of ration 1:0.05 (shown as 50m). when we set the voltage VM1 as input to our oscilloscope with 10 Volts/div and 5ms/division.  We observed the simulated output of the oscilloscope,
we can see that the peak voltage of the sine wave is around 1.1division of the oscilloscope,  therefore the input Voltage from the secondary of the transformer is given by;  1.1 x 10 = 11V.
Proves:


 Now in the Lab 2, we include a diode in the circuit and observe the waveform of the input voltage. 

 Lab 2
In the Lab 2, we have included the diode in the circuit diagram, observing the output voltage waveform in the simulated oscilloscope, we can see that the negative portion of the waveform has be removed, diode only passes the positive portion of the sine wave. It has been half rectified.  

Lets turn the diode the other way round in Lab 3 and observe the output waveform;

Lab 3
we can observe that the diode now passes only the negative portion of the waveform, this obviates our earlier discussions, in this orientation of the diode, it is the negative portion of the input voltage that forward biases the diode. Thus passes only the negative portion of the waveform as shown in Lab 3.

See Simulation Video for half-wave rectifier Lab:

 

Full Wave rectifier using; 

1.  Center-tapped Transformer:

 

 

 Figure 4.10:  Full wave rectifier circuit with center tapped transformer

In this circuit, two diodes which are connected in such a way that only one of them will conduct (i.e. forward biased) for each half of the waveform cycle. A center tapped transformer has its secondary winding split into two equal halves with common center taped connection.

The circuit configuration makes one of the diode to be forward biased in each half of the cycle.

With a full wave rectifier, we have the following relations;

Lab 4: Full wave rectifier with center tapped transformer
In the Lab 4, we can see that the output voltage has a peak amplitude of about half the input at the secondary turn of the transformer. This is because the center tapped has halved the input into two equals, while the flow of current is in such a way that one diode conducts (i.e. forward biased) at a time.

See Simulation Lab Video for full wave rectifier with center tapped transformer:

2.   Bridge Rectifier

Figure 4.11:  Bridge Rectifier
In the bridge rectifier circuit of figure 11, four diodes are configured in the design so that, two of the diodes will conduct electricity for each half of the AC waveform. figure 11(a) and 11(b) depict how current flows in each half of the AC waveform.

The advantage of a bridge rectifier is that, there is no centre-tap and the entire secondary voltage can be used.

 Lab 5: Bridge Rectifier Virtual Lab Simulation

See Lab 5 Video:


 

Sample Question 3:

Assume a 20:1 primary to secondary turns ratio transformer, with a 220V rms input of 50Hz.

i.                    Determine its secondary output.

ii.                  The peak voltage, V_p and the effective DC voltage V_dc

iii.                Also determine the actual voltage across the load using a center-tap and a bridge rectifier.

PREVIOUS LECTURE 

 Electronic Components