Filters (3.16) PDF

Filters (3.16) Learning Objectives 3.16.1 Define the operation and typical uses of low pass filters (Level 1). 3.16.2 Define the operation and typical uses of high pass filters (Level 1). 3.16.3 Define the operation and typical uses of band pass filters (Level 1). 3.16.4 Define the operation and typ...

Filters (3.16) Learning Objectives 3.16.1 Define the operation and typical uses of low pass filters (Level 1). 3.16.2 Define the operation and typical uses of high pass filters (Level 1). 3.16.3 Define the operation and typical uses of band pass filters (Level 1). 3.16.4 Define the operation and typical uses of band stop filters (Level 1). 3.16.5 Identify the basic characteristics of low pass, high pass, band pass and band stop filters (S). 3.16.6 Define the properties that affect the resonant frequency of a circuit (S). 3.16.7 Identify the purpose of a tuned LCR circuit (S). 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 208 of 284 Filter Characteristics Filters Filters are devices that prevent unwanted quantities from passing through a system. A typical example is the car oil filter, which prevents impurities passing into the engine. An electrical filter is similar to the oil filter, but in this case the electrical filter prevents certain frequencies from passing through to the next stage of the circuit. Filters allow you to choose only the desired frequency or band of frequencies and eliminate the unwanted frequencies. The many uses of filters include channel selection in communications, reduction of interference by rejecting unwanted frequencies, and prevention of spurious oscillations. Most electronic equipment contains at least one filter. Filters are classified according to their frequency response characteristics. There are four basic types of filters: Low pass High pass Band pass Band stop. The term band refers to a range of frequencies. Usually, filters pass or reject a band of frequencies rather than a single frequency. Aviation Australia Four basic types of filters characteristics 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 209 of 284 The area under the curve is the allowed (passed) band of frequencies. For accurate sound reproduction, a good set of speakers will include: A tweeter A mid-range speaker A woofer. Sub-woofer A low-pass filter, as its name implies, passes low frequencies but rejects high frequencies. The dividing line between the low and high frequencies is referred to as the cut-off frequency and is denoted as fCO.. Below the cut-off frequency, signals pass essentially unaffected, but frequencies above the cut-off frequency are greatly attenuated or reduced. A high-pass filter passes all frequencies that are higher than a given cut-off frequency and rejects frequencies that are lower than the cut-off. Output from the amplifier is fed to the filter card, where the filter splits audio into: High frequencies for tweeters Medium frequencies for mid-range speakers Low frequencies for woofers. Therefore, only the correct range of frequencies is sent to each speaker. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 210 of 284 Aviation Australia Frequency response of various filters The capacitor in the tweeter line likes to pass high frequency, while the inductor in the woofer line likes to pass low frequency. The capacitor and inductor in the mid-range line likes to pass middle frequency. Aviation Australia Filter circuit for speakers 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 211 of 284 Typical Use of Filters on Aircraft – Vibration Sensor Filters are used to select frequencies. It is essential to selectively monitor aircraft engine vibration but reject taxi rumble or air turbulence. Vibration sensor (a) 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 212 of 284 Aviation Australia Vibration sensor (b) 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 213 of 284 Basic Filter Operation Filter Operation The diagrams below show a low pass filter with a cut-off frequency of 1 kHz. Applying a 10 V peak signal at different frequencies, such as 100 Hz, 1 kHz and 10 kHz, will result in differences. Observe the change in the output. In the top diagram, the filter has a 100 Hz signal applied at 10 V peak. The filter allows the entire signal to pass to the output. In reality, some loss of signal will occur due to the way the components are configured within the filter. This will become clearer later on when we look at filter circuits. For now, these losses can be ignored for the purpose of explaining the filter operation. In the centre diagram, a 1 kHz signal is applied to the filter, again at 10 V peak. Notice that the applied signal is at the same frequency as the cut-off frequency (fco), that is, 1 kHz. The output from the filter is still at 1 kHz since filters do not change the frequency, but the amplitude of the signal has been reduced to 7.07 V peak. Some attenuation has taken place within the filter. Refer back to the previous graph associated with a low pass filter, the output voltage starts to reduce before the cut-off frequency is reached. In the bottom diagram, the frequency of the applied signal has been increased to 10 kHz and the input amplitude remains the same at 10 V peak, but this time filter has reduced the amplitude of the output to 1 V peak. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 214 of 284 Aviation Australia Low pass filter frequency responses 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 215 of 284 Practical Filters In the shaded area of the ideal curves, frequencies are passed. In the unshaded area, frequencies are rejected. The ideal filters are so selective that the output voltage stops completely (low pass) or starts exactly (high pass) at the cut-off frequency. The difference between those signals that will be passed and those that will be rejected is sharp and definite. In practice, such steep and highly selective curves are impossible to achieve. While the ideal can be approached with special components and techniques, most filters introduce gradual attenuation, or loss, with frequency. For example, the practical or true response curve of the low-pass filter is illustrated below. At high frequencies, above fCO, the output voltage decreases gradually as the frequency increases. Hence, attenuation gradually increases at a nearly constant rate, with frequency. Aviation Australia Low-pass filter frequency response The practical response curve of the high-pass filter in the following figure shows that at low frequencies, before the cut-off, output voltage increases gradually as frequency increases. Attenuation gradually decreases, so the output voltage increases at a nearly constant rate with frequency. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 216 of 284 Aviation Australia High-pass filter frequency response RC Low-Pass Filter There are two basic configurations for a low-pass filter: RC or RL. The RC low-pass filter uses a series resistor and a shunt capacitor. Aviation Australia Circuit for an RC low-pass filter In the case of a voltage divider across an AC source, the output is always less than the input; therefore, the filter is also an attenuator. Because inductors and capacitors are frequency sensitive, the output voltage varies with frequency. The inductive reactance (XL ) is proportional to frequency, whereas the capacitive reactance is inversely proportional to frequency. If the capacitive reactance (XC ) is high at low frequencies (compared to the resistance), most of the input voltage appears across the capacitor. However, as the frequency increases, XC decreases. More and more voltage appears across the resistor, while less appears across the capacitor. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 217 of 284 RL Low-Pass Filter Suppose we have an RL low-pass filter that uses a series inductor and a shunt resistor. The inductive reactance (XL ) in the circuit varies proportionately with frequency. At low frequencies, XL is very low (compared to the resistor), so most of the input voltage appears across the resistor. However, as frequency increases, XL increases. More and more voltage appears across the inductor, while less appears across the resistor. This circuit also rolls off the higher frequencies. Aviation Australia Circuit for an RL low-pass filter Summary of Low-Pass Filters In general, an RC low-pass filter will do exactly the same job as an RL low-pass filter with the same cut-off frequency. The roll-off rates will also be the same. However, RC low-pass filters are usually easier to use and less expensive than RL low-pass filters because capacitors come in a wider range of values, are generally smaller than inductors and are cheaper to produce. Aviation Australia Physical filter electronic components 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 218 of 284 High-Pass Filter Operation Introduction to High-Pass Filter Operation A high-pass filter is a frequency-selective circuit that passes all frequencies above the cut-off frequency with little or no attenuation, while it rejects those signals below the cut-off frequency. Such filters are easily constructed with various combinations of resistance, capacitance and inductance. Aviation Australia Frequency response of a high-pass filter RC High-Pass Filter Suppose we have an RC high-pass filter with a series capacitor and a resistor that form a voltage divider across the generator. The filter output is taken from across the resistor. Aviation Australia Circuit for an RC high-pass filter 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 219 of 284 At frequencies below the cut-off frequency, the capacitive reactance (XC ) is very high and most of the generator voltage will be across the capacitor. Very little voltage will appear across the output resistor. However, as the frequency increases, XC decreases. Less voltage is dropped across the capacitor and more and more voltage appears across the resistor, allowing the higher frequencies to pass. RL High-Pass Filter Suppose we have an RL high-pass filter with a series resistor and an inductor that form a voltage divider across the generator. Output voltage is taken from across the inductor. Aviation Australia Circuit for a RL high-pass filter At frequencies below the cut-off frequency, the inductive reactance (XL ) is very low and most of the generator voltage will be across the resistor. Very little voltage will appear across the output inductor. However, as the frequency increases, XL increases. Less voltage is dropped across the resistor and more and more voltage appears across the inductor, allowing the higher frequencies to pass. The output of an RC high-pass filter, at the cut-off frequency (fCO), is 70.7% or 3 dB down from the maximum applied voltage. Performance of RC and RL high-pass filters is typically identical. Above the cut-off frequency, high-pass filters pass signals with little attenuation. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 220 of 284 Summary of High-Pass Filters The performance of RC and RL high-pass filters is generally identical. At frequencies above the cutoff frequency, both RC and RL high-pass filters pass signals with little attenuation. At the cut-off frequency, the attenuation will be 3 dB. At frequencies below the cut-off frequency, the attenuation increases at a rate of 6 dB per octave or 20 dB per decade, which is the same for RC and RL low-pass filters. Aviation Australia High-pass characteristic curve (top right) RC and RL low- and high-pass filters are made with various combinations of inductors, capacitors and resistors. In each case, the filter is really a voltage divider made of two components. One component is a resistor and the other is a frequency - varying component such as an inductor or a capacitor. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 221 of 284 Aviation Australia Summary of circuits and frequency responses - 1 Aviation Australia Summary of circuits and frequency responses - 2 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 222 of 284 Because the output voltage from each filter is tapped from a voltage divider, the output voltage will be less than the input voltage. As the supply frequency changes, the circuit reactance changes, and consequently the voltage division ratio changes. This causes the output voltage to vary. By selecting the appropriate values of resistance and capacitance for the voltage divider, filters can be designed so that they pass or eliminate the desired frequencies. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 223 of 284 Series and Parallel Resonance Series Resonance As you have seen previously, inductive and capacitive reactances in an LCR circuit vary with frequency. An increase in the frequency causes inductive reactance (XL) to increase and capacitive reactance (XC ) to decrease. A decrease in the frequency causes the inductive reactance to decrease and the capacitive reactance to increase. The condition in which the inductive reactance equals the capacitive reactance is called resonance. For every combination of L and C, there is only one frequency (in both series and parallel circuits) that causes XL to exactly equal XC. This frequency is known as the resonant frequency. When the resonant frequency is fed to a series or parallel circuit, XL becomes equal to XC and the circuit is said to be resonant to that frequency and is totally resistive. The circuit is now called a resonant circuit; resonant circuits are tuned circuits. To describe the principles of series resonance we will use the representative series resonant circuit. Aviation Australia Series LCR circuit 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 224 of 284 Circuit Operation Let us now look at the curves which show how XL and XC vary with frequency in a series resonant circuit. The resonant frequency (fr) is the frequency where the magnitude of XL equals the magnitude of XC. Aviation Australia Impedance response for both L and C components It can be seen that below the resonant frequency (fr ), XC is larger than XL, so the voltage across the capacitor is larger than the voltage across the inductor and the series LCR circuit will act capacitively. Above the resonant frequency (fr), XL is larger than XC, so voltage across the inductor is larger than the voltage across the capacitor and the series LCR circuit will act inductively. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 225 of 284 Parallel Resonance The resonant frequency (fr) of a parallel resonant circuit is calculated with the same formula used for series resonant circuits: 1 fR = 2π√ LC An ideal parallel resonant LC circuit is illustrated below. You will notice that the source voltage is applied across each component. Aviation Australia Parallel LC circuit (tank circuit) 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 226 of 284 Tuned Circuits Each LCR circuit responds to resonant frequency differently than it does to any other frequency. Because of this, an LCR circuit has the ability to separate frequencies. For example, suppose the TV or radio station you want to see or hear is broadcasting at the resonant frequency. The LC 'tuner' in your set can divide the frequencies, picking out the resonant frequency and rejecting the other frequencies. Thus, the tuner selects the station you want and rejects all other stations. If you decide to select another station, you can change the frequency by tuning the resonant circuit to the desired frequency. 1. In a series resonant circuit, at resonance, the impedance is resistive and a low value (usually the value of the resistance of the wire in the coil). 2. In a parallel resonant circuit (tank circuit), at resonance, the impedance is resistive and a high value (depending on the values of L and C chosen, it can be almost infinite). If you remember these two facts about tuned circuits, the world of filters is simple. Filters are used to select frequencies 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 227 of 284 Resonant Circuits as Filters Resonant circuits can be made to serve as filters. Series LC circuits (resonant) offer: Minimum opposition to current flow at frequencies at or near resonant frequency Maximum opposition to current flow at all other frequencies. Parallel LC circuits (resonant) offer: Maximum opposition to current flow at frequencies at or near resonant frequency Minimum opposition to current flow at all other frequencies. Using these two concepts, band-pass and band-stop filters can be constructed. The band-pass filter and the band-stop filter are two common types of filters that use resonant circuits. Aviation Australia Band-pass and band-stop responses 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 228 of 284 Band-Pass Filter Introduction to Band-Pass Filter Band-pass and band-stop filters use resonant circuits that you have seen in previous topics. If you have a good understanding of resonant circuits, the operation of band-stop and band-pass filters will be easy for you to grasp. These filters are designed to either reject or pass a narrow range of frequencies and due to this characteristic are widely used in both communication and navigation equipment. A band-pass filter is a circuit that allows a selected range of frequencies to pass, while frequencies above and below this range are greatly attenuated. The two basic configurations for a band-pass filter use either a series resonant LC network or a parallel resonant LC network. Aviation Australia Band-stop characteristic curve (bottom right) 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 229 of 284 Simple Band-Pass Filter In the circuit of figure view (A), the series LC circuit acts as a band-pass filter. It passes currents with frequencies at or near its resonant frequency, and opposes the passage of all currents with frequencies outside this band. Aviation Australia Simple series band-pass (A) View (B) is the parallel-LC circuit. If the parallel LC circuit is tuned to the same frequency as the series LC circuit, it will provide a path for all currents having frequencies outside the limits of the frequency band passed by the series-resonant circuit. You may remember from resonant circuits, series LC resonant circuits offer minimum impedance at resonance, thus passing maximum current. Conversely, parallel LC resonant circuits offer maximum impedance at resonance, thus passing minimum current. Aviation Australia Simple parallel band-pass filter (B) The simplest type of band-pass filter is formed by connecting the two LC circuits as shown in view (C). The upper and lower frequency limits of the filter action are filter cut-off points. 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 230 of 284 Aviation Australia Combination series-parallel band-pass filter (C) Series LC resonant circuits offer minimum impedance at resonance, thus passing maximum current. Conversely, parallel LC resonant circuits offer maximum impedance at resonance, thus passing minimum current. Should any frequencies be delivered to the circuit that are not within the selected bandwidth, not only will the series LC network block them, but the parallel LC network will shunt them away from the load. Aviation Australia Frequency response of a band-pass filter 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 231 of 284 Band-Stop Filter Introduction to Band-Stop Filter A band-stop filter is a circuit that rejects or greatly attenuates signals over a narrow frequency range. It is also known as a notch filter or band elimination filter. As with the band pass filter there are two basic configurations for a band stop filter. These configurations use either a series resonant LC network or a parallel resonant LC network. Aviation Australia Band-stop characteristic curve (bottom right) 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 232 of 284 Simple Band Stop Filters A band-stop filter circuit is used to block the passage of current for a narrow band of frequencies, while allowing current to flow at all frequencies above or below this band. Since the purpose of the band-stop filter is directly opposite that of a band-pass filter, the relative positions of the resonant circuits in the filter are interchanged. The parallel LC circuit shown on the following page view (A), act as a band-reject filter, blocking the passage of currents with frequencies at or near resonant frequency and passing all currents with frequencies outside this band. If a series LC circuit shown in view (B), is tuned to the same frequency as the parallel circuit, it can act as a bypass for the band of rejected frequencies. Then, the simplest type of band-reject filter is obtained by connecting the two circuits as shown in view (C). Aviation Australia Simple series (A) and parallel band-stop filters (B) © Aviation Australia Combination series-parallel band-stop filter (C) 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 233 of 284 As remembered from resonant circuits (at resonance): Series LC circuits offer minimum impedance, thus passing maximum current. Parallel LC circuits offer maximum impedance, thus passing minimum current. For frequencies within the selected bandwidth: Blocked by parallel LC network, and Passed by series LC network (all signals shunted away from load). For frequencies not within the selected bandwidth: Aviation Australia Frequency response of a band-stop filter 2024-02-15 B-03b Electrical Fundamentals CASA Part 66 - Training Materials Only Page 234 of 284