Lattice and bridged-T equalizers are circuits which are used to correct for the amplitude and/or phase errors of a network or transmission line. Usually, the aim is to achieve an overall system performance with a flat amplitude response and constant delay over a prescribed frequency range, by the addition of an equalizer. In the past, designers have used a variety of techniques to realize their equalizer circuits. These include the method of complementary networks; the method of straight line asymptotes; using a purpose built test-jig; the use of standard circuit building blocks,; or with the aid of computer programs. In addition, trial and error methods have been found to be surprisingly effective, when performed by an experienced designer. In video or audio channels, equalization results in waveforms that are transmitted with less degradation and have sharper transient edges with reduced overshoots (ringing) than before. In other applications, such as CATV distribution systems or frequency multiplexed telephone signals where multiple carrier signals are being passed, the aim is to equalize the transmission line so that those signals have much the same amplitude. The lattice and bridged-T circuits are favoured for passive equalizers because they can be configured as constant-resistance networks such as the Zobel network, as pointed out by Zobel and later by Bode. The single word description “equalizer” is commonly used when the main purpose of the network is to correct the amplitude response of a system, even though some beneficial phase correction may also be achieved at same time. When phase correction is the main concern, the more explicit term "phase equalizer" or "phase corrector" is used. (In this case, the circuit is usually an all-pass network which does not alter the amplitude response at all such as the lattice phase equalizer). When equalizing a balanced transmission line, the lattice is the best circuit configuration to use, whereas for a single-ended circuit with an earth plane, the bridged-T network is more appropriate. Although equalizer circuits, of either form, can be designed to compensate for a wide range of amplitude and phase characteristics, they can become very complicated when the compensation task is difficult, as is shown later. A variety of methods has been used to design equalizers and some of these are described below. Several of the procedures date back to the early part of the 20th century when equalizers were needed by the rapidly expanding telephone industry. Later, with the advent of television, the equalisation of video links became very important too.
Amplitude correction The aim of an equalizer network is to correct for deficiencies in the amplitude response of a transmission line, lumped element network or amplifier chain. Equalisation is often necessary with transmission lines and lumped element delay lines which tend to have increasing loss with frequency. Without correction, waveform fidelity is lost, and rise and fall times of transients are degraded (i.e. less sharp). Sometimes amplitude correction is required for more subtle reasons, for example, in the case of analogue colour television waveforms, colour errors can occur in the displayed pictures when the transmission system’s response is not flat. It is usual to choose lattice and bridged-T equalizers which are constant-resistance networks. It was pointed out by Zobel and later by Bode that such networks can be cascaded with each other and with a transmission line or with a lumped element circuit, without introducing mismatch problems. The use of constant resistance configurations has been common practice in equalizer design, for many years, and almost all of the examples presented in this article have this property. Whatever the design method, passive equalizers always introduce additional loss into the transmission path, and this has to be made good by an amplifier or repeater.
The method of complementary networks In some of his early work, Zobel devised a lumped element circuit to simulate the behaviour of a given long transmission line of interest. Such a device was useful in that it allowed investigatory work on a transmission system to be carried out in the convenience of the laboratory. Importantly, as was pointed out by Zobel, once such a network had been designed, it was always possible to find a realizable complementary network, which exhibited the inverse response.
An example The procedure can be illustrated by a simple example presented by Zobel, which is shown below. Here, the left hand lattice has a simple low-pass characteristic and the right hand lattice has the complementary characteristic. For this circuit R1*R2 = L1/C1 = L2/C2 = R0^2 with R1 < 2.R0 . C2 is given by C 2 = [ ( R 0 R 1 ) 2 − 1 ] . L 1 R 0 2 {\displaystyle C_{2}={\Big [}{\Big (}{\frac {R_{0}}{R_{1}}}{\Big )}^{2}-1{\Big ]}.{\frac {L_{1}}{R_{0}^{2}}}}
For a normalized network R0 = 1Ω. Choose R1 = 0.5Ω and L1 = 1H then R2 = 2Ω, C1 = 1F, C2 = 3F, and L2 = 3H The responses of the individual sections and the overall response are shown in the plots for the composite network, given on the right.
This compensation process can be described mathematically, by means of the basic lattice equations given in lattice network, as follows. The transmission loss of a normalized (R0 = 1) constant resistance lattice with through arms Za and cross-diagonal arms of Zb is
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