2 Electronic Components and their properties

2.1 Resistor

For a resistor the voltage dropped across it is proportional to the amount of current flowing on the resistor Vr = I.R ,any current waveform through a resistor will produce the exact same voltage waveform across the resistor, although this seems trivial it is worth keeping it in mind, especially when it comes to dealing with other components such as inductors, capacitors and ordinary wire at high frequency.

2.2 Inductor

The voltage across an inductor Leads the current through it by 90 degrees, this is due to the fact that the voltage across an inductor depends on the rate of change of current entering the inductor. The impedance of an inductor is (w = 2.pi.f), which reflects the fact that the voltage leads the current. This analysis is vital in working out the phase shift trough complicated LC networks.

2.3 Capacitor

The voltage across a capacitor lags the current through by 90o, applying the same logic to the capacitor as was used for the inductor, the reason for this lag in voltage is that the voltage is proportional to the integral of current entering the capacitor. Looking at the above current plot the current will reach a maximum 90O into the cycle, the voltage will reach a maximum when the area under the current’s curve is added up this doesn’t happen until 180O into the currents cycle, giving a 90 degrees voltage lag. The Impedance of the capacitor can be found to be , which also takes into account of the capacitor’s voltage lag.

2.4 Resonant Circuits

In the last section the resistor, inductor & capacitor were looked at briefly from a voltage, current and impedance point of view. These components will be the basic building blocks used in any radio frequency section of any transmitter/receiver. What makes them important is there response at certain frequencies. At high low frequency the impedance of an inductor is small and the impedance of a capacitor is quite high. At high frequency the inductor’s impedance becomes quite high and the capacitor’s impedance drops. The resistor in theory maintains it’s resistive impedance at low & high impedance. At a certain frequency the capacitor’s impedance will equal that of an inductor, This is called the resonant frequency and can be calculated by letting the impedance of a capacitor to that of the inductor’s and then solving for w (angular velocity in radians per seconds) and then finding the resonant frequency Fc (it is normally represented as Fo, but in relation to FM it essentially represents the oscillator carrier frequency) in Hertz.

2.4.1 Series resonant circuit

At low frequencies the capacitor impedance will dominate the overall impedance of the series circuit and the current is low. At high frequencies the inductor impedance will dominate and the current will also be low. But at the resonant frequency the complex impedance of the capacitor will cancel that of the inductor’s and only the resistance of the resistor will remain effective, this is when the current through the circuit will be at a maximum.

2.4.2 Parallel resonant circuit

The parallel circuit above (known as an LC tank) takes the same advantage of the resonant frequency but this time the impedance will be at a maximum and the current will be at a minimum at FC. This due to the fact that the minimum impedance in a parallel circuit dominates the overall impedance of the tank. The impedance will be equal to (R // +jXL // -jXC)

now substituting , cross multiply and bring the common Wc out of the brackets to get the impedance as a function of frequency.

now with the substitution and Wc = 2.pi.fc, the parallel impedance at any frequency can be found. A factor called the Q factor can be introduced which is equal to R/WcL .

at frequencies above resonance f >> fc the above equation evaluates to

Which is capacitive.

At frequencies above resonance f << fC the above equation evaluates to

Which is inductive impedance

At resonance the complex component under the line will be zero, yielding a real value of R which is purely resistive.



Impedance versus Magnitude


Phase Plot

Simulations carried out in Mathcad with values of C = 25.19pF and L = 0.1mH, the resonant (centre) frequency was found to be 100MHz. The Q has a part in finding the bandwidth, BW = FC /Q, which was calculated to be 67KHz with a resistance R = 100KW.

The phase plot show’s a phase of +90 degrees (inductive impedance) before the resonant frequency, 0 degrees (resistive) at resonant frequency, and -90 degrees (capacitive) above the resonant frequency.

2.5 The Q factor

Quality of the component has to be taken into account. The Q factor is a measure of the energy stored to that which is lost in the component due to its resistive elements at low or high frequencies. Inductors store energy in the magnetic field surrounding the device. Capacitors store energy in the dielectric between it’s plates. The energy is stored in one half of an ac cycle and returned in the second half. Any energy lost in the cycle is associated with a dissipative resistance and this gives rise to the Quality factor Q. Q as stated before is the ratio of maximum energy stored to the amount lost per ac cycle. As shown in the previous section the Quality factor determines the 3db bandwidth of resonant circuits.

For a series RLC circuit at Fc

or

For a parallel RLC circuit at Fc

In circuits where there is no Rseries or Rparallel (only an L and a C) the inherent resistive properties of the inductor (skin effect) and capacitor (dielectric permittivity) at high frequencies can be taken into account.

Conclusion : the higher the Q the less energy is dissipated .

2.6 High frequency response of discrete components

2.6.1 Wire

The resistance of a piece of wire decreases as the diameter of the wire increases, where P is the resistivity, L the length of the wire and A is its cross sectional area. But beyond a particular frequency the resistance of the wire increases, strong magnetic fields are built up at the centre of the wire due to high frequency ,this force pushes the majority of the charge carriers (electrons) away from the centre and towards the outside of the wire. So now there is less available cross sectional area for the carriers have to move along the wire, therefore the resistance increases at high frequencies. This phenomenon is known as the "skin effect", when the magnetic field at the centre increases and local inductive reactance takes over.

Analysing the skin effect further, it is understood that AC current distributes itself across the cross sectional area of the wire in a parabolic shape, simply put means that the majority of the carrier lie in the outside, while few remain at the centre of the wire. The outside region where most of the electrons reside can be defined as the distance in from the outside where the number of electrons has dropped to (2.7183)^-1 = 36.8 % of the electrons on the outside.

2.6.2 Inductor

Since wire is the main ingredient of inductors and since the resistance of wire increases with increasing frequency, therefore the losses of an inductor will increase with increasing frequency ( as characteristic resistance increases). The amount of loss for a given inductor through dissipation the inverse of the Q factor.

Therefore, since Rseries increases with frequency, therefore the Q factor will decrease with increasing frequency. Initially, the Q factor of the inductor increases at the same rate as the frequency changes and this continues as long as the series resistance remains at the DC value. Then, at some frequency that depends on the wire diameter and also on the manner of the windings, the Skin effect sets in and the series resistance starts to climb. However not at the same rate as the frequency does, and so the Q continues to rise, but not as steeply as before. As the frequency increases further, a stray capacitance begins to build up between adjacent turns. Along with the inductance a parallel resonant circuit is formed and the resulting resonant frequency causes the Q factor to start decreasing.

2.6.3 Capacitor

The resistive element in a capacitor at a high frequency is brought about by the material in between the plates of the capacitor, which inherently controls the permittivity and then also the conductive properties of the capacitor at high frequencies. The dissipation factor of the capacitor is also the inversely associated with the Q factor. The efficiency in capacitors at high frequencies are generally better than the inductor as regards the Q factor, but other considerations such as the added series inductance of the leads and the internal capacitor plates will greatly effect the efficiency of the capacitor. Good RF techniques are usually used to combat this by keeping the leads short when soldering a capacitor into a circuit.

2.7 Temperature stability of the Tank

The temperature coefficient (TC) of a device is the relative change in one of its parameters per degree Celsius or Kelvin. The units are usually in parts variation per million per degrees Celsius (ppm/°C). Taking the case of an oscillator (with an LC tank) the TC is the fractional change of frequency over the centre frequency per 1°C temperature change. Usually the TC for any given component or system is given, to find the change in frequency for a given temperature change, simply multiply the TC by the temperature change and the centre frequency (frequency the oscillator should be running at).
An oscillator will always change frequency due to temperature change, because its components have non-zero temperature coefficients. One of the offenders would be the capacitor. The capacitance is normally worked out by C = (e.A) / d, where e is the permittivity of the dielectric between a capacitor’s plates, A is the common surface area that the plates overlap across the dielectric and d is the distance between the plates. One of the best tuning capacitors available is the silvered mica capacitor (often called the chocolate drop, because of it's smooth brown oval appearance). The variation of centre frequency of an oscillator will now be looked at with respect with capacitance change.
now differentiate with respect to C and then solve for dfc by multiplying across by dC. Then dividing across by fc will yield
if the capacitance change due to temperature or any other ageing effects is less than 10%. Looking at the equation, it becomes apparent if a 2% increase in capacitance occurs, then a 1% decrease in centre frequency shall take place. This seems trivial but when large frequencies are involved, i.e. 100MHz a 1% change is -1MHz, which is a change of 5 channels down in the commercial bandwidth.

The junction capacitance of the transistor (section 2.9) which aslo sets the center frequency, is also a major source of frequency instability due to temperature change.

2.8 Discrete components to be considered for use in a High frequency circuit

2.8.1 Resistors

Fixed and variable resistors form the basic components in any electronic circuit, therefore they shall be the first component that will looked at, followed by Capacitors and finally Inductors.

The three main factors when choosing a resistor for an intended application are

The Table below gives a standard overview of the types of resistors used and their specifications

note: if you do not have the font symbol installed on your computer, the resistor values will be followed by a W instead of the Greek Omega, to denote Ohms
Thick Film Metal Film Carbon Film Wire-wound
Max. Value 1MW 10MW 10MW 22KW
Tolerance ±1% to ±5 ±1% to ±5 ±1% to ±5 ±1% to ±5
Power Rating 0.1 to 1 Watt 0.125 to 0.75W 0.125 to 2W 2.5 W
Temp. Coeff. ±100 to 200ppm/°C ±50 to 200ppm/°C 0 to 700ppm/°C ±30 to 500ppm/°C
Stability V. Good V. Good V. Good V. Good
Typical Use for accurate work Accurate work General purpose for low values

2.8.2 Capacitors

Capacitors as mentioned before in a previous section are made up of two conducting plates with a dielectric in between. The most important factors when choosing a capacitor are
Silvered Mica Ceramic Electrolytic Tantalum Polystyrene
Range 2.2pF to 10nF 1nF to 100nF 0.1mF to 47mF 1mF to 100mF 22pF to 0.1mF
Tolerance ± 1% -20% to 80% -10% to 50% ±20% ±1%
Temp. Coeff. +35ppm/°C +20% t -80% ±1500 ppm/°C ±500 ppm/°C -150ppm/°C
Leakage resistance Very High High Very Low Low Very High
Stability Excellent Good Fair Good Excellent

  1. Silver Mica

    2. These capacitors have excellent stability and a low temperature coefficient, and are widely used in precision RF ‘tuning’ applications

  2. Ceramic types

    3. these low cost capacitors offer relatively large values of capacitance in a small low-inductance package. They often have a very large and non-linear temperature coefficients. They are best used in applications such as RF and HF coupling or decoupling, or spike suppression in digital circuits, in which large variations of value are of little importance

  3. Electrolytic Types

    4. These offer large values at high capacitance density; they are usually polarised and must be installed the correct way round. Aluminium foil types have poor tolerances and stability and are best used in low precision applications such as smoothing filtering, energy storage in PSU’s, and coupling and decoupling in audio circuits.

  4. Tantalum types

    5. Offer good tolerance, excellent stability, low leakage, low inductance, and a very small physical size, and should be used in applications where these features are a positive advantage.

  5. Poly Types

    6. Of the four main ‘poly’ types of capacitor, polystyrene gives the best performance in terms of overall precision and stability. Each of the others (polyester, polycarbonate and polypropylene) gives a roughly similar performance and is suitable for general purpose use. ‘Poly’ capacitors usually use a layered ‘Swiss-roll’ form of construction. Metallised film types are more compact that layered film-foil types, but have poorer tolerances and pulse ratings than film-foil types. Metallised polyester types are sometimes known as ‘green-caps’

  6. Trimmer capacitors

    7. Polypropylene capacitors are ideal variable capacitors, a fact due to the polypropylene dielectric having a high insulation resistance with a low temperature coefficient. The polypropylene variable capacitor comes in a 5mm single turn package, which is suitable for mounting directly on to a PCB. The typical range of capacitance involved would be from 1.5pF to 50pF.

2.8.3 Inductors

There are two types of inductors that can be discussed, and they are
  1. Manufactured inductor

    2. When choosing an inductor from a manufacturer, the core in the coil and the over all Q factor will have to be taken into account. The core should preferably be made of soft ferrite which will in turn minimise the energy losses of the inductor and therefore increase the Q factor. The ferrite core can be adjusted to give a slight change in inductance
  2. Self made inductor

    3. Inductors can be easily wound around air cored formers, there are a number a various manufactured air cored formers on the market. Self made inductors are very useful when a particular inductance is desired.
    where
    L = inductance in mH
    d = diameter, in inches
    b = coil length, inches
    N = number of turns

2.9 NPN Transistor

PNP bipolar and P channel J-Fets are widely used at low frequencies, the preference for high frequency systems lies with the NPN and N channel J-Fets. This is due to the electrons being the majority carriers in both the BJT’s and J-Fet’s conduction channel. The NPN BJT is the most commonly used and for the rest of this discussion will be the transistor that will be focused on.

2.9.1 High Frequency Response

The most interesting property is the junction capacitances from the base to emitter and base-collector, the figure in the previous sub-section shows that for the 2N3904, the base-emitter capacitance is larger than the base-collector, because of heavier extrinsic doping and it’s forward biasing the depletion region is naturally smaller than the base-collector’s. As the frequencies are increased the two capacitances will drop. Because the capacitors are effectively in series, the smaller one dominates (base-collector capacitance). The capacitances are also influenced by the rate of change in base current magnitudes.

A resistance exists of typically in the order of tens of ohms at the base, this parasitic is caused by impure contact between the base’s polysilicon to silicon junction. This coupled with the r’e resistance and the current gain makes up the input resistance of the transistor. Rin = b( Rbase + r’e) ; as stated previously the r’e will inevitably drop as the frequency increases, therefore Rin(base) will inevitably be equal to b( Rbase). This makes the system rather unstable as R(base) is essentially a parasitic impedance. To increase stability Re, (which is normally RF bypassed), will have to be introduced.

Another inherent flaw which might be used to some advantage in the high frequency response of the NPN model, is that of output collector signals are be fed back to the base. This increases the likelihood of continuos oscillation at high frequencies. The importance of this flaw can be seen when oscillators are being discussed in section 3.5.

2.10 Transistor Amplifiers

Now that the basic electronic components have been considered, a look at the 3 transistor amplifiers is worthwhile prelude to the next section, which contain references and examples of these amplifiers. The three amplifiers are called Common Emitter, Common collector and Common Base.

2.10.1 Common Emitter

r’c and r’e are the junction resistances at the collector and emitter respectively. r’c is seen as infinite (reverse bias junction), r’c is equal to the threshold voltage Vt divided by the emitter current.

IC = IB + IE, IB the base current is relatively small compared to IC Þ IC» IE

All capacitor's used here are DC opens and AC shorts. The supply ideally has no impedance and therefore no voltage dropped across it. So it is an AC ground.

DC Analysis

Voltage at the base, Vb = {R2 / (R1 +R2)}.Vcc Voltage at the Emitter, Ve = Vb - 0.7. Emitter Current, Ie = VE / (RE1 + RE2) » IC, Voltage at collector, VC = VCC - (IC.RC) Voltage across the collector and emitter, VCE = VC - VE

AC Analysis

2.10.2 Common Collector (emitter follower)

DC analysis is similar to the common emitter.

AC Analysis

2.10.3 Common Base

DC analysis is similar to the common emitter.

AC Analysis