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

Varactor Diode

Varactor Diode

A varactor , also known as tuning diode, a variable capacitance diode, a varicap diode or variable reactance diode, is a diode that exploit the principle of operation of semiconductor diode, to act or behave like a variable capacitor i.e. has variable capacitance, which is a function of the external voltage impressed on its terminals. As we know that a capacitor is basically a device constructed using two parallel plates (conductor) separated by an insulator or a dielectric (insulator) (See: Basic Electronic (Passive Component)).

If we reconsider the electrical characteristics semiconductor diodes as in figure 3.15.

Figure 3.15: Semiconductor diode

The P-side is a good conductor owing to the presence of excess holes; also the N-side is a good conductor due to the presence of excess free electrons. The depletion layer is ridden of charge carriers thus an insulator. This can be likened to the construction of a typical capacitor. 

 

 Figure 3.16: Semiconductor Diode depicted as a capacitor

Also, we will recall that when diode is forward biased, the width of the depletion region becomes narrower with respect to the external voltage supply, the more the voltage the narrower is the depletion region, until the voltage overcomes the built-in barrier and allow current flow.

We can also recall also that; the Capacitance of a capacitor is Proportional to the area A of the plate and inversely proportional to the distance d between the plate in an equation given by;

            ε₀ – permittivity in free space

            ε_r  - dielectric constant (relative permittivity)

            A – area of the plate

            d – distance of plates apart

(See:  Basic Electronics (Passive Components)).

Now, employing the semiconductor diode as a capacitor, the area A of the plates (P and N-sides) can be increased, by reducing the depletion layer (distance d, between the plates) through applying an external voltage of a certain level, thus increasing its capacitance, while we can reduce its capacitance by reducing the applied voltage which increases their distance apart (depletion region) and reduces the cross sectional each sides (P- and N-) of the diode. This means that the capacitance is varied with respect to the applied voltage, thus provides the variable capacitor property and called a Varactor.

See Also:

Light Emitting Diode (LED) 

Photo-diode           

Photo-diode

Photo-diode

This is another type of diode, it is also a semiconductor diode designed in such a way which, when exposed to light, generates a potential difference or change its electrical resistance. In its operation, when photons of light falls on the semiconductor diode, electrons absorbs energy from the photons, become photo-excited and jump into the conduction band, also leaving holes in the valence band, transport of the free electrons and holes increases the electrical conductivity of the material, when an external voltage is applied it results in a current flow. This is known as Electron-hole photo-generation in the semiconductor diode.

Figure 3.13: Electron-hole photo-generation in Semiconductor diode.

Figure 3.14:   Symbol of a photo-diode.

The circuit symbol of a photo-diode is similar to that of an LED just that the arrows points inward in the case of a photo-diode.

The photo-diode operates in the reverse bias mode, even though is a semiconductor diode and we know it will impose a very high resistance to the flow of current in reversed biased, this is to ensure that the current observed in a circuit involving a photo-diode is solely due to the intensity of the incident light, i.e. photons energy.

Photo-diodes has many applications in electronics design; an example of which is an Opto Isolator.

In some circuit we may need to electrically isolate two different parts of the circuit, i.e. there should be no connections at all but we may still want what happens in one of the circuit to have an effect on the other.

Figure 3.13:  Opto Isolated Circuits

 For example the circuit in figure 3.13, when voltage Vs changes, the intensity of LED L also varies and in essence varies the intensity of light falling on the photo-diode P, which in-turn changes resistance of the photo-diode and this can be detected at V₀. Therefore, though the circuit is perfectly isolated with reference to electrical connections, but through light beam they are connected, this is called and Opto-isolator.

See Also:

Light Emitting Diodes (LED)
Varactor Diode

Light Emitting Diodes

Light Emitting Diode (LED)

LEDs are common semiconductor diodes used in many applications today. They emit a fairly narrow bandwidth of light, which can be either visible light at different coloured wavelengths, invisible infra-red light used in remote controls or laser light when they are in forward biased connection in a circuit. It is important to study the working principles of this device because of its various found applications in electronics.

LEDs Applications

-          They are used in displaying numbers in digital clock and some digital instruments.

-          Transmission of information from remote controls

-          As power indicator in appliances

-          There collections form images on jumbo Television screen and illumination of traffic lights.

-          Tiny LEDs are been used to replace the tubes that light up Liquid Crystal Display (LCD) High Definition Television (HDTs) to make very slim televisions.

Construction and Principle of Operation

Instead of the vacuum emitting light source like incandescent bulb or emission of light from gas like the compact fluorescent light bulb,  an LED emits light from a piece of semiconductor material.

The historical discovery of light emission capabilities of semiconductor material, dates back to 1907, when electrical engineer Henry J. Round touched a crystal of silicon carbide found near Niagara Falls with two wires connected to a battery. He reported that on applying 10V between two points on the silicon carbide crystal, the crystal gave out a yellowish light. Though not realised at that time Henry J. Round had operated the first crude solid-state lamp, the light emitting diode.

The light emission mechanism of this semiconductor material is of paramount importance in sense that, most electrical light sources such as incandescence of a hot electrode, luminescence of a glowing plasma, or fluorescence of a phosphor coating, are capable of producing exceedingly high luminous outputs, but each of the conventional light sources is unsuited to a broad range of potential applications because of their slow response time, inherent fragility, and short lifetime.

The LED eliminates these set backs of conventional lamps with its solid-state reliability, speed, and compact size.

Figure 3.6: Symbol of a Light Emitting Diode (LED)

Theory of LED’s operation

The LED is essentially a P-N junction diode.  To realise the light emitting property in most commercial LEDs, they use a heavily doped n and slightly doped p junction.

Figure 3.7:  Unbiased pn⁺ junction diode (the superscript + on the n indicates and heavily doped n-side).

For better understanding of the principle behind LEDs, let’s consider and unbiased pn⁺ junction shown in figure 3.7. The depletion region extends mainly into the p-side because it contains lesser charge carrier due to the fact that it was slightly doped as explained earlier. The potential barrier V₀ prevents the excess free electron on the n+ side form diffusing into the p-side.

Now, if the pn+ junction is forward biased, as in figure 3.8, at V≥V₀, electron from n+ side gets injected into the p-side. But the holes injection from the p side to the n+ side is very less and so the current is primarily due to the flow of electrons into the p-side. These electrons injected into the p-side recombine with the holes. This recombination results in spontaneous emission of photons (light). Noting that the energy of emitted photons is given by; E_g =  E_c-E_v, Ec is the energy of electron in the conduction band, E_v energy of electron the valence band, E_g energy required for an electron to jump form the valence band to the conduction band, (See;Basics of Semiconductor devices) .This effect is called injection electroluminescence. These photons are allowed to escape from the device without being reabsorbed, thus gives the illumination observed in LEDs.

Figure 3.8: Forward biased pn⁺ junction

The wavelength of the photons of light emitted is derived from the relation shown in the figure 3.8 i.e.  Eg = hv, Eg is the Energy gap, h, is planck’s constant and v, the frequency of the emitted light.

            v = c/λ   c is the speed of light and λ  is the wavelength.

Therefore;

The wavelength λ of the emitted light determines the colour of light emitted by the LEDs. Thus given the value of planck’s constant h = 4.135 ×10^-15 eV and speed of light c =3×10⁸m/s, we can determine the wavelength and thus the colour of light emitted by a semiconductor, through its energy gap E_g.

   

For example a semiconductor with band-gap of 3.5eV will emits light of;

 

Given an approximate wavelength of different colours of light as in table 3.1 bellow;

Table 3.1

Color	Wavelength (nm)
Red	780 - 622
Red	780 - 622
Orange	622 - 597
Yellow	597 - 577
Green	577 - 492
Blue	492 - 455
Violet	455 - 390

 

Using table 3.1, then the light emitted by the semiconductor in our example is violet colour.

LEDs in Electronic Circuit

 Using an LED in a circuit, it normally requires about 10mA of current for a bright glow and has about 1.7V across its terminals. Hence, when we connect a 6V power supply to it, we must include a resistor in series to drop the excess 4.3V i.e. (6-1.7)V.

For example in the circuit bellow;

Figure 3.9: LED in a circuit.

To determine the value of R to be connected in the circuit above, we can see that R and the resistance of the LED R_LED and thus share the voltage input 6V.

The voltage required across R_LED is 1.7V, therefore the voltage needed to be dropped by R is 4.3V.  Also since R and R_LED are in series, the same current is passing through them i.e. 10mA (require for LED bright glow).  

Note that, for V_R (the voltage across R) to be equall 4.3V and I_R (current through R) equal 10mA, we need R value given by;

 
 

The value of R required in the circuit in figure 3.9 is 430Ω.

If you reverse the connection of the 6V battery in the connection of the circuit in figure 3.9, you’ll realise that the LED will not glow at all, this proves that the LED is a diode, i.e. allows the flow of current in only one direction.

 Seven Segment Display

A very common application of LEDs in electronic equipments and devices is in Seven Segment Display. The technique used in applying LED in a seven segment display is to arrange the LED in form of figure 8, as shown in figure 3.10 bellow;

Figure 3.10: Seven Segment LED display

All the 7-segments in figure 3.10 are individual LEDs labelled a – g. They com in two connections, either in a common anode or common cathode connection see figure 3.11a (common anode) and 3.11b (common cathode).

Figure 3.11: LED connections in 7-segment display

In the common anode, all the anodes of each LED are connected together and to the positive pole of the battery (Vcc), while each of the LED is switched on/off individually by connecting to the negative pole of the battery (GND) through the 430Ω resistor with their corresponding switch a to g.

While in the common cathode, the cathode of all the LEDs are connected together and to the negative pole of the battery (GND) through 430Ω resistor for each of the LED. The LEDs are switched on/off individually by connecting to their anode to the positive pole of the battery (V_cc) with their corresponding switch a to g.

The idea behind the 7-segment display is that, by selectively glowing (switched ON) the LEDs a to g, we can generate all the numbers we want from 0-9. See figure 3.12.

 

Figure 3.12: Using 7-Segment LED to display number 0-9.


See Also:
Photo-diode
Varactor Diode