Low-pass LC filters are recognized by having the inductor (or inductors) in series with the signal path and the capacitors shunted across the signal path. The lowpass filter (LPF) attenuates all signal frequencies above its cutoff and passes all frequencies below the cutoff.
(A) Three-element, T-section low-pass filter and
(B) three-element, pi-section low-pass filter.
Figure 1 shows two basic single-section LPFs. The t-filter configuration is shown in Fig.1A, and the pi-filter configuration is shown in Fig. 1B. The values of the capacitors and inductors are calculated using the equations:
(1)
(2)
These equations will also be used to calculate the values of the components in the other filters as well, although the numbering of the constants (K) will be different. The values of constants K1 and K2 are found from Table 1.
Table 1. Filter design constants for Fig. 1
Example: Calculate the component values for both t-filter and pi-filter configurations for a low-pass filter with a cut-off frequency of 35 MHz.
The inductors should be single components, wound, or selected and set for the specific inductance required. The capacitors, on the other hand, can be made up from several capacitors in series and parallel in order to obtain the correct value. Remember when doing this, however, that tolerances can make the whole thing less than useful. Most capacitors have tolerances of 5 or 10%, unless otherwise noted. It is best to use as close a value capacitor as possible, and that could involve handselecting capacitors, according to actual capacitance using a meter or bridge.
The inductors can be either homewound or purchased. Although it’s possible to use adjustable inductances and capacitances in these filter circuits, it is not recommended that they be adjusted in the circuit. The adjustable components can allow one to obtain the specific values called for in the equations, but they should be preset to the value prior to being connected into the circuit. This job can be done using either a LC bridge or a digital LC meter, such as are found on some digital multimeters.
Each section of the filter provides a certain degree of attenuation, as indicated by the steepness of the roll-off slope beyond the cutoff frequency. Cascading sections will increase the roll-off slope, so they will also increase the attenuation obtained at any given frequency in the stopband.
The design of inductor-capacitor (LC) filters for radio frequency (RF) circuits is often presented in its most arcane mathematical form. Use of that design approach allows you to optimize designs. However, this form is also above the capabilities of many people who could put filters to good use. A different approach is needed, and that approach is the normalized 1-MHz model. In this design approach, a model is built by calculating the component values for 1 MHz. The component values can be scaled for any frequency by dividing the 1-MHz value by the desired frequency, expressed in megahertz.
A limitation on this approach is that it assumes that the input and output impedances are both equal to 50 Ohm (i.e., the design impedance of the 1-MHz model filter). Because RF systems tend to have 50-Ohm impedances; however, this restriction does not pose a big problem in most cases.
A filter must be constructed properly if it is to work correctly. The two main factors to consider are layout and shielding.
Proper layout involves two main issues. First, keep the output and input ends of the circuit physically separated so as to prevent coupling of signal energy between them. Second, make sure that all inductors in the filter are shielded, arranged at right angles to each other, or wound on toroidal cores. All three of these approaches are used because they reduce coupling between inductors. Shielding keeps the magnetic field of the coil contained within the metallic shield. When cylindrical, solenoid-wound coils (i.e., those with a length greater than the diameter) are placed at right angles with respect to each other then magnetic coupling is minimized. A toroidal coil form is doughnut shaped and it naturally contains the magnetic field because of its geometry.
Shielding of the entire filter circuit is necessary to keep outside signal energy from getting into the filter and to ensure that the only signal reaching the load (i.e., the circuit being driven by the filter) has passed through the filter circuit. Figure 1 shows a sample filter (such as those covered in this chapter) enclosed within a shielded box. The signal input and output jacks. (J1 and J2) are coaxial connectors.
The box should be either a die-cast aluminum box with a tight-fitting lid (some brands are pretty sloppy, so be careful), a sheet-metal aluminum box with overlapping lips for a RF seal, or a box specifically intended for RF work (these can be identified by the RF “finger” gaskets around the edge of the cover).
1.Filter success often depends on layout and construction. Shielded enclosures are a must!
Figure 2 shows several different types of filter applications. In Fig.2A, the filter is placed between the antenna and the antenna input of a receiver. Its function is to remove unwanted signals before they reach the front end. Whether a high-pass, low-pass, or bandpass filter is used depends on the local situation (i.e., the frequencies that you wish to eliminate).
(A) ahead of a receiver antenna input to reduce unwanted signals,
There are several good reasons for using a filter ahead of a receiver, even when the strong local signal is not within the normal passband of the receiver. The narrow passband selectivity of the receiver is set in the IF amplifiers and the RF (“frontend”) selectivity is a lot broader. As a result, strong signals often reach the input stage, which will be either an RF amplifier or mixer. In either case, the unwanted signal can drive the input of the receiver into a nonlinear region of operating, creating either harmonics or intermodulation distortion products. These spurious signals not only are audible in the receiver (in some combinations), but also take up part of the receiver’s dynamic range.
Figure 2B shows a filter placed at the output of an oscillator circuit. If the output signal is a pure sine wave, it will contain only one frequency (i.e., the desired oscillation frequency). But if there is even a little distortion, then harmonics will be present. These harmonics will adversely affect some circuits that the oscillator drives, so they must be eliminated.
(B) at the output of oscillators and other waveform generators
The most usual filter used on oscillator outputs is the low-pass filter. The filter is designed with a cutoff frequency that is between the desired fundamental frequency and its second harmonic.
Another type of filter is a very high-Q bandpass filter. These filters are very narrow. The purpose of using such a filter is to reduce the phase noise on the oscillator signal. It takes a very narrow-band filter to do this trick, and both the oscillator frequency and the passband of the filter must be stable or the poly will be unsuccessful.
The circuit in Fig. 2C shows the use of two filters at the output of a double
balanced mixer (DBM). The DBM receives two input frequencies, F1 and F2, and will output a spectrum of mF1 +- nF2, where m and n are integers greater than 1 (on non-DBM mixers, m and n might be 1, indicating that F1, F2, or both may appear in the output). It is not sufficient to pick off the signal in the desired band and reject the signals in the unwanted band. Those unwanted signals will be reflected back into the mixer and might adversely affect its operation. The proper strategy is to use a circuit that passes the undesired signals to a dummy load that has a resistance equal to the mixer output impedance. This arrangement allows the dummy load to absorb the unwanted signals rather than permits them to reflect back into the mixer circuit.
(C) at the output of a double balanced mixer in a diplexer impedance-matching circuit.
Filters are frequency-selective circuits that pass some frequencies and reject others. Filters are available in several different flavors: low-pass, high-pass, bandpass, and notch. All of these filters are classified according to the frequencies that they pass (or reject). The breakpoint between the accept band and the reject band is usually taken to be the frequency at which the passband response falls off -3 dB. The four different types are characterized below.
Low-pass filters pass all frequencies below the cutoff frequency defined by the -3-dB point (Fig A). These filters are useful for removing the harmonic content of signals or eliminating interfering signals above the cutoff frequency.
(A) low-pass
High-pass filters pass all frequencies above the -3-dB cutoff point (Fig.B). These filters are useful for eliminating interference from strong signals below the cutoff point. For example, a person using a shortwave receiver might wish to install a 1800-kHz high-pass filter to eliminate signals from strong AM broadcast stations.
(B) high-pass
Bandpass filters pass all frequencies between lower (FL) and upper (FH) -3-dB points, while rejecting those outside the FH–FL range. Bandpass filters are either wideband (low Q) or narrow band (high Q), as shown in Fig.C and D, respectively.
(C) bandpass
(D) narrow bandpass
(E) notch or band reject
Q is the quality factor of the bandpass filter and is defined as the ratio of the center frequency to the bandwidth. For example, if a filter is centered on 10,000 kHz, and it has a 25-kHz bandwidth between the lower and upper -3-dB points, then the Q is 10,000/25 =400
Notch filters (band reject filters), pass all frequencies except those between lower and upper cutoff frequencies (Fig E). Some notch filters are made broad, but many are very narrow. The latter are designed to suppress a single frequency. For example, a local FM broadcast signal will often interfere with television or two-way radio services. A notch filter tuned to that frequency will wipe it out. Similarly, on an AM band receiver, if it is being desensitized by a strong local station, reducing reception of all other frequencies on the AM band, a single-frequency notch filter can be used to suppress that one station’s signal, leaving the other frequencies untouched.
