From the Ground Up
Eric Edwards GW8LJJ completes his overview of inductors.
Eric Edwards GW8LJJ completes his overview of inductors.
Last time we looked at a notch filter, which is used to remove unwanted frequencies or bands of frequencies. In this, the final part of Inductance and Inductors, we will look at the other types of filters used for RF (Radio Frequencies). These are BPF (Band Pass Filter), LPF (Low Pass filter) and HPF (High Pass Filter). In the diagram, Fig. 1, showing the four different types of filters the vertical axis represents the amplitude of the signal and the top is usually labelled as 0dB, which means no attenuation. The amplitude level drops as the line drops to the bottom and this is marked in negative dB (−dB) to show the amount of attenuation (signal level drop). The horizontal axis shows the frequency increase from left to right. The filter ‘cut-off’ (reduced output at unwanted frequencies) amplitudes are measured at the −3dB points, in other words, it is when the signal drops to half, so it is better to have the −3dB point before the first harmonic.
The LPF shows it passing signals at the top (start) of the vertical axis, which will be 0dB and as the frequency increases (travels along the horizontal axis) the signal starts to drop in amplitude. Where this is at the −3dB point, it is considered end of the wanted frequency. The HPF does the opposite so it has no output until it reaches the wanted frequency, so removing any unwanted frequencies below it. The BPF is a combination of HPF (at the start) and LPF at the end so only allowing a band of frequencies to pass. The Band Stop (notch filter) is the exact opposite in operation to the BPF. It stops any signals within a given bandwidth to pass. It notches them out.
In all radio circuit designs there are filters. It could be said that radio receivers and transmitters are collections of filters and amplifiers. The simplest of receivers, the ‘crystal’ set, uses a filter to tune in the wanted stations and normally uses a ‘rejector’ tuned circuit that removes, or attenuates other signals.
This type of receiver has no amplifiers, of course, and relies on a good rejector filter for its selectivity. It is all to do with ‘resonance’.
Resonance
A tuned circuit is said to be resonant when it is sensitive to a particular frequency, and insensitive to all others. To explain further, in earlier parts of this series we learned that a coil (inductance) has opposition to changes of current, which is called inductive reactance. As the frequency increases so does the inductive reactance whereas a capacitor has a resistance to voltage, called capacitive reactance, which gets smaller with an increase in frequency. Because the inductor has a resistance to AC (RF) current, the current lags behind the alternating voltage. The capacitor does the opposite, so that the current leads the voltage. The inductor and capacitor are opposite each other in that respect. The combined effect of inductive and capacitive reactances is known as impedance and, at resonance, the impedance is (close to) zero at the resonant frequency.
RejectorTuned Circuits
The rejector tuned circuit is a capacitor in parallel with a coil. The values of both are set to allow all signals except the wanted signal to pass through. Fig. 2 shows a rejector circuit used in a basic crystal set. L1 is the inductor and C1 the capacitor, which is variable to select the required stations. This ‘tuned circuit’ works by allowing all unwanted signals to pass through to the ground (earth) connection and allowing the wanted signals to reach the diode (detector). The wanted frequencies are allowed to bypass the tuned circuit because it is at high impedance when at resonance. In this case, resonance is achieved when the inductive reactance and the capacitive reactance are the same and this provides high impedance (resistance) to the wanted frequency so it does not flow through the coil to ground. The tuned circuit is a rejector circuit as it rejects all unwanted frequencies getting to the diode.
The rejector, or parallel, circuit has current flowing in the inductor and capacitor but they
are out of phase with each other because the current in the inductor lags behind the current into the capacitor. The current (RF signal) will flow into the capacitor plates and charge it. When it is fully charged and cannot receive any more voltage, it discharges through the inductor and will now charge the capacitor by the current flowing into the other plate of the capacitor, which will be in the opposite direction.
This charging and discharging will be at the rate of the incoming frequency and will continually charge and discharge in this resonant circuit building up a high oscillating voltage. This creates very high impedance at the resonant frequency.
Acceptor Tuned Circuit
An example of an acceptor tuned circuit can be seen in Fig. 3. It is sometimes called a series resonator as the inductor and capacitor are in series. As the impedance of the inductor rises with frequency and the capacitor decreases with frequency there is a point where the two are equal and cancel out each other. The impedance at the resonant frequency is therefore zero and the required frequency, which is therefore allowed to pass through. It will have high impedance at all other frequencies. This is the opposite effect to the rejector tuned circuit.
Mutual Inductance
When two coils are in close proximity to each other, an EMF (Electro Motive Force) in one coil creates an EMF in another closely coupled coil such as in a transformer.
From Wikipedia, the free encyclopaedia: Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday’s law of induction. Lenz’s law describes the direction of the induced field. Faraday’s law was later generalised to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism. Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.
In a mains transformer the primary has the household mains connected to it and the secondary produces a voltage appropriate to the ratio of the two windings. In other words, if the secondary winding is smaller in the number of turns relative to the primary winding, the output will be a smaller voltage than the input. A typical transformer with a lower secondary winding is used in a low voltage power supply. Similarly, if the secondary windings have more turns than the primary windings, the voltage across the secondary windings will be greater and this can be used to step up the voltage from say, 110V to 240V. Fig. 4 shows three transformers with different primary-to-secondary winding ratios. One with equal windings on both primary and secondary is a 1:1 ratio and will produce the same voltage at the secondary windings as placed in the primary windings. This type is usually called an isolation transformer and is used, for example, to isolate the household mains from the mains earth. The neutral power line coming into the building is linked to the earth so without isolation there is not only a high voltage potential across the live to neutral but also a high voltage between live and the earth connection. The isolation transformer removes (isolates) the earth connection. There is a high (mains) voltage across the secondary winding but not from any of them to an earth point. There are two other transformers in Fig. 3 with one that has a smaller number of turns on the secondary and a third showing a larger secondary winding. This is a step-up transformer where a larger voltage is taken from the secondary compared to the voltage at the primary. A typical type will be used where a high voltage power supply is needed for valve power amplifiers, with its output being many hundreds or even thousands of volts.
RadioTransformers
In Fig. 5 there are two transformers connected ‘back-to-back’ − the secondary of each transformer is connected to the other. The primary of the left-hand transformer has a signal connected and the right-hand transformer has the same frequency signal but much larger. This is taking advantage of the principles of mutual inductance and the rejector tuned circuits. Fig. 6 is the actual setup used. In this example, the transformers are 45µH types and the capacitors are 39pF each. The input is taken from a signal generator with a scope lead connected on channel two of a scope and tuned to 1.5MHz. The output from the second transformer has a scope lead connected to channel one on the scope. The transformer cores are adjusted (peaked) for
maximum output from the right-hand transformer. Mutual inductance takes place as in normal transformer action and the transformers are rejector circuits so that the output is greater in amplitude than the input for the reasons explained in the rejector paragraph. Fig. 7 shows the two waveforms. Both the ‘Y’ amplitudes are set at 5mV per division. The input signal is 5mV and the output is almost 20mV so a large difference in levels with no amplifiers other than the ‘passive’ transformer tuned circuits. Both ’Y’ inputs on the scope are set to 1MΩ impedance. Normally when transformers are used as input from the antenna to the receiver, the antenna is connected to the lower windings and the higher windings are ‘tuned’ to the required frequency by making the coil high resistance (impedance) to the wanted signal to flow to ground. Two transformers (or more) are used for what is referred to as a bandpass filter (BPF).
Bandpass Filter
Bandpass filters are used in various places in receivers and transmitters to reject unwanted frequencies. A typical place is at the antenna input of a receiver to select particular bands of frequencies. Usually, a pair is used for each band, either with fixed tuning or variable tuning of the larger windings. The smaller windings for the receiver ‘front end’ are more suited for a 50Ω input and outputs, Fig. 8. A pair of 45µH transformers (TOKO KANK 3333 equivalent) is used, with a parallel 150pF capacitor across each coil and a coupling capacitor 47pF between the coils for the 160m band. It is broad-banded to fully cover the band. The parallel capacitors (150pF) can be replaced with a twin-gang variable capacitor to enable peaking on any part of the band. This is particularly useful when using a BPF as the input to 40m or a higher band, to make the receiver more sensitive in any one part of the band and for attenuating interfering near signals. A 160m AM (Amplitude Modulation) monitor ‘crystal set’ can be made easily using a pair of 45µH transformers and a twin variable capacitor. Fig. 9 shows a circuit using two of the transformers and a ganged capacitor. The receiver antenna is connected to the higher winding via C1, 100nF capacitor. The ganged capacitor can be any that is to hand. The larger the value, the wider the band coverage and a 500pF for VC1 and VC2 will cover from 1MHz to 2.5MHz so will cover the medium wave (MW) band as well as 160m. Using smaller capacity gangs (VC1 and VC2 at 300pF) will reduce the total bandspread and lower values (say 150pF each gang) will reduce it even more, perhaps choosing values to tune only Topband or maybe just for MW coverage. The diode (detector) can be any Germanium type − an OA90 or OA81 work very well.
Diode Conduction
You will have been taught (or told) that a Germanium diode conducts when the ‘barrier’ voltage is greater than 200mV (0.2V). If that were strictly correct, the crystal set would not work. The diode conducts at much lower applied voltage with very low current but will not pass higher levels of current until the barrier voltage has been reached. What this means is that if the diode is connected to a load so that higher than very low off-air signal level current can pass through, then the barrier voltage theory applies. However, if the load is very light (tens of kΩ) there will be very low current allowed to pass through (Ohms Law). This is the reason for using high impedance headphones at the output of diode. If lower resistance headphones (3Ω, 16Ω, 30Ω etc) were used, current will not flow so no signals will be received. If high impedance headphones are not available, the output of the diode can be connected to an amplifier via a 100nF (not critical value) capacitor and signals can then be heard.
Lowpass Filter
Lowpass Filters are used for stopping or greatly attenuating signals above a certain frequency. They allow low frequency signals to pass but not higher frequencies. Low frequency in this context can be RF frequencies and not just audio. It refers to ‘lower’ frequencies to pass and limiting the flow of higher frequencies. A typical example of an LPF is at the output of a transmitter to help prevent out of band radiation. Fig. 10 is displaying a 14MHz (20m band) LPF with a dB (decibel) level scale on the left-hand side. At the top of the graph it can be seen that the line is at 0dB and the line curves downwards to show the attenuation in dBs. At 20MHz it is −3dB (between 0dB and −6.599dB), so all frequencies above 14MHz are attenuated with 50MHz being at approximately −40dB. The circuit for this filter is at Fig. 11 and is comprised of ‘standard’ inductors and capacitors. The impedance from the transmitter’s antenna output is 50Ω, so a resistor of that value is represented in the design at the input to the filter along with a representing terminating resistor at the output. In both cases the resistors are
not there physically as they are the impedances of the antenna terminal of the transmitter and the antenna. The capacitors (100pF) at both ends are the same values along with the inductors (620nH = 0.62µH), which means the filter can be used either way round. The filter was designed with ELSIE (see Ref) and it was designed to use ‘standard’ capacitor and inductor values. Another typical use for an LPF is to change square waves to sinewaves.
SquareWaves
Square waves can be useful in RF circuits for providing signals on amateur bands that are harmonically related, for example the harmonics of 1.8MHz are 3.6MHz, 7.2MHz, 14.4MHz and 28.8MHz. These are called even harmonics as they are ‘even’ multiples of the fundamental signal.
Of course, each harmonic will be weaker than the original but they are still useful for checking other bands on a receiver. Harmonics are also used in frequency multiplier circuits where the fundamental is changed to a second, third or higher harmonic to produce a higher band. The others, including the fundamental frequency, are naturally filtered out by the ‘tuned’ multiplier circuit. Third (odd) harmonics are three times the fundamental and their multiples. There are many harmonics and they are created by saturation of an oscillator circuit. The transistor or other ‘active’ device is switched hard-on (saturated) and fully-off (cut-off), which produces on-off pulses that are square in shape as seen on a scope. The transistor is turned on and after a very short duration is switched off again depending on the frequency of the oscillator, and thus produces the square wave.
Square to Sine
There will be a need to remove the harmonics when a clean signal is required as in a signal generator or VFO (Variable Frequency Oscillator) because it can otherwise cause spurious (emissions) signals that are not wanted and undesirable. This is where the LPF comes into use again as it can remove frequencies above the wanted one. The square waves contain lots of frequencies above the fundamental as explained earlier, so the LPF can be used to remove those not wanted. The LPF is designed to ‘cut off’ before the start of the first harmonic (even). Fig. 12 shows a square wave with its fundamental frequency as 3.550MHz but as it is square it will have multiple other frequencies. This can be seen at Fig. 13 on a spectrum analyser, where many harmonics can be clearly seen. Putting this signal through a LPF designed to cut off before the first harmonic, the result at the output can be seen at Fig. 14 (spectrum analyser) and a clean sinewave can be seen on the scope at Fig. 15. A suitable multiband LPF for the HF amateur bands is shown at Fig. 16 and is used at the output of a transmitter. Commercially built transceivers will have all the BPFs and LPFs built-in but home-brewed transmitters must have an LPF for each band used to avoid out of band radiation.
Highpass Filter
Highpass filters are used where there is a need to remove frequencies below the wanted one. In older ‘vinyl’ record players, they were commonly used to remove low frequency ‘rumble’ usually picked up from the turntable.
The ‘scratch’ filter was an LPF to remove high frequency noises collected from the scratches on the records. Direct conversion receivers are susceptible to picking up local mains hum and other low frequency noises, so one is placed at the front end (antenna input) of the receiver.
Reference
ELSIE the filter design program. Tonne Software.