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For DC we know power is voltage times current, and we should also know that we can apply this to something like an AC mains powered bar heater, in which the heating coil is not overly inductive, with reasonable accuracy. It also applies to a fan heater, in which the motor current is trivial compared to the element current, and where the element often zig-zags, so is even less inductive.
However, if we have a large textile factory, where the primary load is the motors of the looms, the current will lag the voltage, giving a poor power factor. This means that current flows in and out of the motors windings with some of it not doing work. The angle of the lag determines the power factor.
The power company will be unhappy about having to supply current which is not doing work, and so not being charged for if a standard meter is used. Off the exam, when inductive loads, such as motors and transformers are lightly loaded, the power factor generally becomes worse. Also, the current which flows due to a poor power factor does cause I²R losses in building, street cabling, and transformers.
The power factor is calculated as the Cosine of the phase angle. The first 90 degrees of a cosine wave starts at 1, and declines towards 0 at 90 degrees, following the curve of the second 90 degrees of a sine wave. If the value is negative, the same power factor (the same cosine value) is produced as if it were a positive value. In other words, -30 degrees, like +30 degrees, is around 0.866. The value must between 1 (purely resistive) and 0 (purely reactive). Real world power loads tend to have some inductive component, so a PF of between maybe 0.7 and 0.95.
Apparent power is measured in VA, or Volt Amps. You may have seen a large ground-mounted street transformer marked 750 kVA, or a range of transformers marketed by their VA value, such as 300 VA toroidal units to power large audio amplifiers. The typical "pole pig" ranges from a few tens of kVA to a few hundred. This is because it is the amps flowing in the load which heats the windings. So, if the load is a non-inductive resistor, VA can equal the power of the load in watts, but if the load is inductive, or capacitive, this is not the case.
When doing the cosine (or other calculations), ensure your calculator is set to degrees, often indicated by a "DEG" sign; or by the lack of a "RAD" marker, indicating Radians.
There are 2π radians in one circle, and rotation velocity or frequency can be indicated in radians per second, marked with a lower case omega, ω. You will this see ω replacing 2π𝑓 in formulas such as: XL = 2π𝑓L = ωL. Radians per second also used in Physics, in place of RPM.
As a reminder, we key in 30 and press [COS] to get a value, which if necessary, we can multiply by volts and amps.
Off the exam, the power company supplying our factory may require we place large power factor correction capacitors. These may be the size of a midi-tower PC. Smaller units are used inside fluorescent lamps in businesses and colleges, to correct for the large inductance in the ballast. Ceiling fans in commercial premises also contain them. All these capacitors, if older, may contain oily Polychlorinated Biphenyls, or PCBs, a significant toxin and pollutant.
Also off the exam, but some libraries lend out what are claimed to be power meters. They are however some sort of current meter, using an assumed or measured voltage to display what is actually Volt-Amps, failing to take PF into account. Thus the small capacitive current flowing in the lead to a lamp will show as power consumption, even though this will NOT turn a proper power meter.
Power is simply the number of volt-amps multiplied by the power factor: P = E × I × Cos ϕ
The other way to have a poor power factor is if the load has a large capacitive component. One example is when the capacitive reactance is used to limit current flow in place of a resistor in LED lamps used at mains voltages (a small, lower value resistor is often still used). In reality they probably just partially correct out inductance elsewhere in the house (motors, transformers, etc).
Several important values are:
| Angle | Exact | Decimal | Comment |
| 0 | 1 | 1.0 | Purely resistive |
| 15 | (√6 + √2) / 4 | 0.9659 | Similar to 14° on previous page |
| 30 | √3 / 2 | 0.8660 | |
| 45 | √2 / 2 | 0.7071 | Also 1 / √2 |
| 60 | 1/2 | 0.5 | |
| 75 | (√6 - √2) / 4 | 0.2588 | |
| 90 | 0 | 0 | Purely reactive |
The pulled question asked the power factor of an R-L circuit having a 30 degree phase angle between the voltage and the current? Using a calculator in degrees mode you find that COS 30 = 0.866025404.
We may remember that a position on a map can be described as being 5 kilometres north, and 8 kilometres east of our position; or we can say that it is 9.434 km away, on a bearing of 57.995 degrees.
It is important to remember that while we can describe an antenna as having an impedance of 56+j27 at one frequency, at another it may be 47-j12, and thus the antenna tuner will need significantly different compensation elements. While this may be more noticeable using an antenna on different Amateur bands rather than across a single one, within the AM broadcast band, which has a ratio of over 1:3 in frequency, if we wish to combine two transmitters into one mast, we need fairly complex matching networks, and for 5-10 kW the coil might be the size of a 8 to 10 litre paint tin.
Figure E5-1 shows a graph with real (X) and imaginary (Y) axis. The real, resistive, component must be positive, placing points in the right (green) side of the graph. The imaginary or reactive component may be positive if the reactive part is inductive, and negative if it is capacitive.
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Points in the red area are not possible.
Also, as the inductive or capacitive components in the questions have a fairly large reactance at the frequencies used, only points 1 to 4, near the edges, are the valid answers.
A randomly added question added deals with graphing frequency response, although the logarithmic aspect appears to be the motivation, as that appears in the section title.
Sometimes we want to be able to read what is happening at 20 vs 50 Hz as well as 18 vs 20 kilohertz. If we used used a linear 0 to 20,000 Hz scale on a 20 cm wide graph 100 Hz would be just 1 mm wide, so useless for the first part of the task. Instead each decade has an equal portion, 0 to 100, 100 to 1000, 1000 to 10,000, and a limited section going to 20 kHz or a little more. Within a decade, say 100 to 1000, 100 to 200 is fairly broad, 200 to 300 less so, down to a narrow 900 to 1000.
Decibels are a logarithmic system, so -10 is a tenth of the zero value, -20 is a hundredth, -30 a thousandth.
As an extension you can graph things like microphone or speaker efficiency by frequency, likewise speaker impedance. Another is SWR vs frequency, although for a narrower range, say 144 to 148 a linear scale is fine.
However, where I think they are heading is graphing filter or tuned circuit response. You may want to demonstrate flat passband response across a ham band, but good attenuation above and blow the band, and at harmonics of the band.
Before viewing the site below: While these exams focus on power levels when using dB. However, you likely understand that doubling voltage causes a doubling in current, and taking the voltage into account, 4 times the power. 10 times the voltage is 100 times the power. A tenth of the voltage in a hundredth of the power. These are +6 db, +20 dB, and -20 dB.
If you square root 0.5 you get a value just over 0.7071. A voltage of 0.7071 of the reference level is half the power, or the -3dB point. It is a number you see recurring.
You can see such a graph here: Open University: Normalised first-order low-pass filters
Another example is lower down the page at: RB: Magnitude response
Another graph is here: Decreasing renewable energy costs. Each mark is an approximate doubling.
For a particular material as frequency increases current flow moves to the surface or skin of the material. This means that resistance has a greater impact. It also means that the inside of large coax can be copper tube. While mostly an RF thing, if you read specifications for power cable used in the street, or for wider distribution, the current rating is greater at DC than AC.
Skin depth at a certain frequency can very significantly depending on the metal used.
I read that using "Copperweld" or similar copper-clad steel wire for antennas for 10 metres is great, as the current flows in the copper, but at 3.5 MHz, resistance of the underlying iron core comes into play, and pure copper is better. Silver plating within coax also used in critical applications, such as aviation, and on coils in some tank circuits.
You likely remember that the typical wirewound resistor has inductance which make them unsuitable for use at RF.
The insulation or air gaps between windings of an inductor have a small capacitance.
Capacitors and their leads have some inductance, depending on the type. Capacitors made from rolls of metalised plastic film are an example. The examiner also indicates that they can suffer from "skin effect" above their intended frequency. For electrolytic capacitors inductance is a limiting factor preventing use in RF circuits.
Perhaps skin effect could be caused by the conductive material used in the capacitor, such as if it is nickel, with a very thin skin.
Both these factors can lead to "self resonance". This is reduced by choosing the components with parameters appropriate for the frequency of use. The datasheet for most inductors will specify a self resonant frequency, as well as the frequency or frequencies at which the other parameters are measured. Factors such as being air-cored or wound on ferrite or other material are also listed. They can also be created using a spiral of PCB track.
For RF ceramic or mica capacitors are more common.
Such components are also important in switchmode power supplies and power control systems, which typically operate in the 25 to 100 kHz range. This prevents a whistle or whine being audible, as was the case in tube based TVs with a 15.625 kHz (PAL/SECAM) or 15.750 kHz (NTSC) line freequency.
These are interesting small inductors, consisting of a flattened section of copper: WÜRTH High Current Air Coil and appear like they would have a fair bit of inter-winding capacitance. The self-resonant frequency, fres is listed to the right. It appears that they are designed for use above 4 MHz, but not in the high UHF range. These WÜRTH Air Coil items have round wire, so less capacitance between windings, and often a higher fres.
As frequency increases the lengths of leads can become significant portions of a wavelength. Even at 23 cm (1296 MHz) a 1 cm lead means a 15 degrees phase shift. It also means care has to be taken with lead lengths if paralleling active devices in RF power amplifiers at VHF+.
On microwave gear special surface mounted components are typically used.
This article partially answers "What is an RF capacitor?". Clearly they sell capacitors with copper rather than nickel as the "plates".
These are the actual questions from the Extra licence exam pool, as published by the NCVEC.
E5C01
Which of the following represents pure capacitive reactance of 100 ohms in rectangular notation?
A. 0 - j100
B. 0 + j100
C. 100 - j0
D. 100 + j0
Capacitance has a negative sign, and is indicated by the "- j100" element of the expression, answer A.
E5C02
How are impedances described in polar coordinates?
A. By X and R values
B. By real and imaginary parts
C. By magnitude and phase angle
D. By Y and G values
By magnitude and phase angle, answer C.
This is the "distance and bearing" of the electronics world.
E5C03
Which of the following represents a pure inductive reactance in polar coordinates?
A. A positive 45 degree phase angle
B. A negative 45 degree phase angle
C. A positive 90 degree phase angle
D. A negative 90 degree phase angle
Inductive means a positive angle, and purely ractive means 90 degrees, so +90°, answer C.
E5C04
What type of Y-axis scale is most often used for graphs of circuit frequency response?
A. Linear
B. Scatter
C. Random
D. Logarithmic
This is Logarithmic, answer D.
E5C05
What kind of diagram is used to show the phase relationship between impedances at a given frequency?
A. Venn diagram
B. Near field diagram
C. Phasor diagram
D. Far field diagram
Phase relationship just might be shown on a phasor diagram. Yes, it is answer C.
E5C06
What does the impedance 50–j25 represent?
A. 50 ohms resistance in series with 25 ohms inductive reactance
B. 50 ohms resistance in series with 25 ohms capacitive reactance
C. 25 ohms resistance in series with 50 ohms inductive reactance
D. 25 ohms resistance in series with 50 ohms capacitive reactance
The real component is 50, and that represents the resistance of 50 ohms, and the imaginary (j) component is the reactance, and being negative, this is capacitive; so 50 Ω resistive and 25 Ω capacitive reactance, answer B.
E5C07
Where is the impedance of a pure resistance plotted on rectangular coordinates?
A. On the vertical axis
B. On a line through the origin, slanted at 45 degrees
C. On a horizontal line, offset vertically above the horizontal axis
D. On the horizontal axis
As there is no reactive component, the point is on the horizontal axis, answer D.
E5C08
What coordinate system is often used to display the phase angle of a circuit containing resistance, inductive and/or capacitive reactance?
A. Maidenhead grid
B. Faraday grid
C. Elliptical coordinates
D. Polar coordinates
The term "phase angle" is the indication that this is is polar coordinates, answer D.
Faraday Grid (while perhaps this distractor was riffing off a "Faraday cage") was the name of a potentially fraudulent, and failed UK registered company offering vapourware in power grid control marketplace. Maidenhead locators are used by mostly VHF DXers, and Elliptical coordinates are a real thing, with a Wikipedia article. A Faraday cage can be metal sheet, or nesh, and prevents signals entering or escaping from a room or enclosure.
E5C09
When using rectangular coordinates to graph the impedance of a circuit, what do the axes represent?
A. The X axis represents the resistive component and the Y axis represents the reactive component
B. The X axis represents the reactive component and the Y axis represents the resistive component
C. The X axis represents the phase angle and the Y axis represents the magnitude
D. The X axis represents the magnitude and the Y axis represents the phase angle
The horizontal X axis is the resistive component and the vertical Y axis is the reactive component, answer A.
E5C10
Which point on Figure E5-1 best represents the impedance of a series circuit consisting of a 400 ohm resistor and a 38 picofarad capacitor at 14 MHz?
A. Point 2
B. Point 4
C. Point 5
D. Point 6
This is a capacitor, so its reactance must be negative on the vertical (Y) axis, and 400 on the X axis, and the only point appearing to fit this is Point 4, answer B.
However, we better prove it, as if the frequency and capacitance were both large, then Xc would be close to zero (around Point 6).
XC = -1/(2π𝑓c) = -1 / (2xπ × 14×106 × 38×10-12) = -1 / 6.283185 × 0.000532 = -1 / 0.003342655 = -299.16 ohms.
E5C11
Which point in Figure E5-1 best represents the impedance of a series circuit consisting of a 300 ohm resistor and an 18 microhenry inductor at 3.505 MHz?
A. Point 1
B. Point 3
C. Point 7
D. Point 8
Being inductive, the Y component must be positive, and the resistance (the X axis) is 300, so there are two possible choices.
XL = 2π𝑓L = 2 × π × 3505000 × 18×10-6 = 6.283185 × 63.09 = 396.406 ohms, so point 3, answer B.
E5C12
Which point on Figure E5-1 best represents the impedance of a series circuit consisting of a 300 ohm resistor and a 19 picofarad capacitor at 21.200 MHz?
A. Point 1
B. Point 3
C. Point 7
D. Point 8
Being Capacitive, the Y component must be negative, and the resistance (the X axis) is 300, so it can only be point 1, answer A.
XC = -1 / (2π𝑓C) = -1 / (2 x π × 21200000 × 19×10-12) = -1 / (6.283185 × 4.028×10-4) = -1 / 2.530867042×10-4 = -395.15071312 ohms.
E5D01
What is the result of skin effect?
A. Resistance increases as frequency increases because RF current flows closer to the surface
B. Resistance decreases as frequency increases because electron mobility increases
C. Resistance increases as temperature increases because of the change in thermal coefficient
D. Resistance decreases as temperature increases because of the change in thermal coefficient
Kicking in to a limited extent at mains frequencies, as the frequency increases, the current flows in a thinner and thinner layer, closer to the surface, and is significant at high-HF bands, and up, answer A.
E5D02
Why is it important to keep lead lengths short for components used in circuits for VHF and above?
A. To increase the thermal time constant
B. To minimize inductive reactance
C. To maintain component lifetime
D. All of these choices are correct
Component leads in a VHF+ circuit become inductive factors, so need to be kept short, answer B.
E5D03
What is the phase relationship between current and voltage for reactive power?
A. They are out of phase
B. They are in phase
C. They are 90 degrees out of phase
D. They are 45 degrees out of phase
Current in a purely reactive circuit is 90 degrees out of phase, answer C.
My sister had the leads to table lamps turned off (Australia has switches on its outlets), and she said it was because she had borrowed a device touted as a "power meter", and it indicated that power was being consumed. Clearly is was a "guess meter" simply multiplying current and voltage, with no reference to phase angle, as a spinning disc meter does. Thus it reads the wattless current as power, when it is at 90 degrees out of phase with the voltage (and Cos 90 is 0). The spinning disc meter includes a capacitor to neutral which cancels the inductive reactance in the voltage sense coil, ensuring it measures power, not VA, so this current would not register.
E5D04
Why are short connections used at microwave frequencies?
A. To increase neutralizing resistance
B. To reduce phase shift along the connection
C. To increase compensating capacitance
D. To reduce noise figure
Say at 10 GHz, the wavelength is a mere 3cm, so a few millimetres in like a lead metres long within an HF radio, something avoided in all but the most massive transmitters, and so at these frequencies, even a lead a few millimetres would cause a phase shift, answer B.
At 47 GHz a wavelength is just 6.3 mm!
E5D05
What parasitic characteristic causes electrolytic capacitors to be unsuitable for use at RF?
A. Skin effect
B. Shunt capacitance
C. Inductance
D. Dielectric leakage
While values of the smallesst electros and the largest ceramic capacitors almost overlap, the inductance in electrolytic capacitors makes them unsuitable, answer C.
E5D06
What parasitic characteristic creates an inductor's self-resonance?
A. Skin effect
B. Dielectric loss
C. Coupling
D. Inter-turn capacitance
Each turn of an inductor consists of metal and either an enamel insulator, or an air gap in proximity to other conductors of otther turns of the coil, causing capacitance. This is termed inter-turn capacitance, and can lead to resonance, answer D.
E5D07
What combines to create the self-resonance of a component?
A. The component's resistance and reactance
B. The component's nominal and parasitic reactance
C. The component's inductance and capacitance
D. The component's electrical length and impedance
Come capacitors consist of a Swiss roll like structure of a foil or metalisation and a plastic dielectric, so have some inductance, while we discussed inter-turn capacitance above. In either case the reactance from it it being a capacitor, and of the reactance of the parasitic inductance interact; or the inductive reactance of the inductor and the reactance of the parasitic capacitance interact. This can lead to resonance answer B.
In each case it is likely this occurs at frequencies above that intended frequency of the devices involved. This may cause parasitic oscillations or spurious emissions.
E5D08
What is the primary cause of loss in film capacitors at RF?
A. Inductance
B. Dielectric loss
C. Self-discharge
D. Skin effect
These often consist of a rolled structure, and skin effect can cause losses, answer D
These are appropriate at mains or audio frequencies, not RF.
E5D09
What happens to reactive power in ideal inductors and capacitors?
A. It is dissipated as heat in the circuit
B. Energy is stored in magnetic or electric fields, but power is not dissipated
C. It is canceled by Coulomb forces in the capacitor and inductor
D. It is dissipated in the formation of inductive and capacitive fields
The energy "sloshes" between the magnetic and electric fields, meaning between the coil and the capacitor, answer B.
E5D10
As a conductor's diameter increases, what is the effect on its electrical length?
A. Thickness has no effect on electrical length
B. It varies randomly
C. It decreases
D. It increases
When an antenna element is made thicker (perhaps for strength) this makes it effectively longer, answer D.
For HF beams you might calculate the length of elements, determine the size of tubing needed, then re-run the design software with the tube (or truss) size. For 40 metres or lower frequencies triangular truss may be needed.
E5D11
How much power is consumed in a circuit consisting of a 100-ohm resistor in series with a 100-ohm inductive reactance drawing 1 ampere?
A. 70.7 Watts
B. 100 Watts
C. 141.4 Watts
D. 200 Watts
P = I²R = 1² x 100 = 1 x 100 = 100 watts, answer B.
Note that, save for slight losses due to the resistance of the copper, etc, in inductors, power is only dissipated in resistors. No matter what the surrounding components are doing, 1 amp through the resistor causes the same dissipation. There would however need to be greater than 100 volts across the entire circuit to drive this current through the resistor.
The phase angle of the entire circuit is 45 degrees, and PF is 0.7071. Thus A and C are trying to catch out people who apply this. C is the overall apparent power, and the number the number of volts AC applied.
E5D12
What is reactive power?
A. Power consumed in circuit Q
B. Power consumed by an inductor's wire resistance
C. The power consumed in inductors and capacitors
D. Wattless, nonproductive power
This is wattless, nonproductive power, answer B.
If you want to drill on PF:
What is the power factor of an R-L circuit having a 60 degree phase angle between the voltage and the current?
A. 1.414
B. 0.866
C. 0.5
D. 1.73
Firstly, you can ignore anything outside the 0 to 1 range, but COS 60 (degrees) is 0.5, answer C.
How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100-VAC at 4 amperes?
A. 400 watts
B. 80 watts
C. 2000 watts
D. 50 watts
This is P = E x I x Cos ϕ = 100 x 4 x 0.2 = 400 / 5 = 80, answer B.
How many watts are consumed in a circuit having a power factor of 0.6 if the input is 200VAC at 5 amperes?
A. 200 watts
B. 1000 watts
C. 1600 watts
D. 600 watts
A question designed to be answered without a calculator, as 200 × 5 is 1000 VA, and this multiplies by 0.6 to become 600 watts, answer D.
Microstrip consists of precision printed circuit conductors above a ground plane that provide constant impedance interconnects at microwave frequencies. They are printed on special PCB material, to provide constant impedance interconnects on microwave boards.
In serious equipment the substrate / insulation material can be Alumina (Aluminium Oxide) or a ceramic. At these frequencies U-shaped tracks and similar features can be used as filters, and importantly, corners in the tracks must have 45 degree bevels, as otherwise the signal bounces back!
In Australia, with the current blame-game on power prices (and lying about the cost of renewables), remember that 9.091% of the price you pay is the right-wing mob's GST! The same concept (but a different figure) applies in other countries with consumption tax such as VAT, MOMS, GST, etc.
Congratulations: You are now about half-way through the questions.
On to: Components 1 - Semiconductor materials & devices; Diodes
You can find links to lots more on the Learning Material page.
Written by Julian Sortland, VK2YJS & AG6LE, July 2025.
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