Electronics Made Easy - a Complete Introduction to Electronics - Martin Denny [4]
Xc = 1/2pfC Xl = 2pfL
A circuit will exhibit its minimum ac resistance (impedance Z) when Xl = Xc, and the power in the circuit W = VA (the product of V*I). The power factor of a circuit is the relationship between power W and VA.
Power Factor = W/VA
The impedance of a circuit (Z) can be calculated by using Pythagoras Theory:
Z = Ö(R2 + X2)
When a sinusoidal waveform is passed through a bridge rectifier the resultant waveform is the positive half of the sine wave with the mirror image of the negative half added (full wave rectification). The resultant waveform will have a Time T = 1/2f and a voltage of 1.414Vrms - 1.2V (voltage drop across the diode bridge) as shown below in fig 3.
If a smoothing capacitor is connected across the positive and negative terminals of the bridge in parallel with the resistive load the resulting voltage ripple can be calculated as follows:
As P = VI = I2R and Energy E = QV and Pt = VIt then:
QV = VIt therefore Charge Q = It
as charge Q can be expressed as CV then CV = It and V = It/C
The result of smoothing on a full wave rectified voltage is shown below in figure 4. The resultant ripple is shown superimposed on the bridge output without smoothing.
The power supply is shown with a resistor R (the load). The maximum output with no load Vo max = 1.414V - 1.2V, where V is the transformer output in volts rms. The transformer will have a known droop factor at full load, given in percentage of rated output. The power supply dc output will be further reduced by the level of voltage ripple.
SEMICONDUCTORS
SEMICONDUCTOR MATERIALS
Semiconductors are termed active components as the name suggests they exhibit a high or low impedance dependant upon current flow.
The most common forms of semiconductor are silicon and germanium, in their pure form they behave as an insulator and are said to be an intrinsic semiconductor. The relatively low conductivity of an intrinsic semiconductor can be increased considerably by the introduction of impurities. These impurities have the property that their atoms nearly fit into the crystal structure of the semiconductor.
N-type Semiconductors
If a pentavalent impurity element such as arsenic or antimony is introduced into say a germanium crystal only 4 out of 5 valence electrons in each atom are used in forming covalent bonds with the surrounding germanium atoms. The 5th electron even at relatively low temperatures will acquire enough energy to break away and increase the conductivity of the material (electron rich). In N-type materials the impurity atoms become positive ions, which are fixed and an equal number of electrons are able to move about in the crystal.
P-type Semiconductors
Intrinsic semiconductor atoms may be displaced by atoms of trivalent elements such as indium, gallium or boron. In this case there is an incomplete valence band leaving a hole which may be neutralised by an electron moving into it from a nearby bond (electron poor). The hole can move at random and therefore acts as a positive charge carrier. The holes are the majority carriers in this material.
The P-N Junction
The P -N junction refers to the boundary between two types of semiconductor where the material is in effect a single crystal. The formation of the junction causes some holes from the p material and some electrons from the n material to diffuse towards each other and combine. The positive charge on the n side and the negative charge on the p side form a potential barrier. The potential difference across the barrier is sufficient to prevent the movement of both holes and electrons.
Reverse Bias
If a P-N junction is reverse biased the depletion layer is increased. The electrons are attracted towards the positive terminal whilst the holes are attracted towards the negative terminal. When the barrier potential is increased in this way the junction is said to have reverse bias applied.
Forward Bias
If a P-N junction is forward biased the electrons in the N-Type material are then attracted