thumb The thumb is the first digit of the hand, next to the index finger. When a person is standing in the medical anatomical position (where the palm is facing to the front), the thumb is the outermost digit. The Medical Latin English noun for thu ...

The bridged-T delay equaliser is an electrical

all-pass filter An all-pass filter is a signal processing filter that passes all frequencies equally in gain, but changes the phase relationship among various frequencies. Most types of filter reduce the amplitude (i.e. the magnitude) of the signal applied to i ...

circuit utilising bridged-T topology whose purpose is to insert an (ideally) constant delay at all frequencies in the signal path. It is a class of

image filter An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...

Applications

The network is used when it is required that two or more signals are matched to each other on some form of timing criterion. Delay is added to all other signals so that the total delay is matched to the signal which already has the longest delay. In television broadcasting, for instance, it is desirable that the timing of the television waveform synchronisation pulses from different sources are aligned as they reach studio control rooms or network switching centres. This ensures that cuts between sources do not result in disruption at the receivers. Another application occurs when

stereophonic sound Stereophonic sound, or more commonly stereo, is a method of sound reproduction that recreates a multi-directional, 3-dimensional audible perspective. This is usually achieved by using two independent audio channels through a configuration ...

is connected by landline, for instance from an

outside broadcast Outside broadcasting (OB) is the electronic field production (EFP) of television or radio programmes (typically to cover television news and sports television events) from a mobile remote broadcast television studio. Professional video c ...

to the studio centre. It is important that delay is equalised between the two stereo channels as a difference will destroy the stereo image. When the landlines are long and the two channels arrive by substantially different routes it can require many filter sections to fully equalise the delay.

Operation

The operation is best explained in terms of the

phase shift In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it ...

the network introduces. At low frequencies L is low impedance and C' is high impedance and consequently the signal passes through the network with no shift in phase. As the frequency increases, the phase shift gradually increases, until at some frequency, ω₀, the shunt branch of the circuit, L'C', goes in to resonance and causes the centre-tap of L to be short-circuited to ground.

Transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...

action between the two halves of L, which had been steadily becoming more significant as the frequency increased, now becomes dominant. The winding of the coil is such that the secondary winding produces an inverted voltage to the primary. That is, at resonance the phase shift is now 180°. As the frequency continues to increase, the phase delay also continues to increase and the input and output start to come back into phase as a whole cycle delay is approached. At high frequencies L and L' approach open-circuit and C approaches short-circuit and the phase delay tends to level out at 360°. The relationship between phase shift (φ) and time delay (T_D) with angular frequency (ω) is given by the simple relation, :

\phi = \omega T_D \,

It is required that T_D is constant at all frequencies over the band of operation. φ must, therefore, be kept linearly proportional to ω. With a suitable choice of parameters, the network phase shift can be made linear up to about 180° phase shift.

Design

The four component values of the network provide four

degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

in the design. It is required from image theory (see

Zobel network : ''For the wave filter invented by Zobel and sometimes named after him see m-derived filters.'' Zobel networks are a type of filter section based on the image-impedance design principle. They are named after Otto Zobel of Bell Labs, who pub ...

) that the L/C branch and the L'/C' branch are the dual of each other (ignoring the transformer action) which provides two parameters for calculating component values. Equivalently, every transmission

pole Pole may refer to: Astronomy *Celestial pole, the projection of the planet Earth's axis of rotation onto the celestial sphere; also applies to the axis of rotation of other planets * Pole star, a visible star that is approximately aligned with th ...

, ''s''_p in the

s-domain In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the co ...

left half-plane must have a matching zero, ''s''_z in the right half-plane such that ''s''_p=−''s''_z. A third parameter is set by choosing a resonant frequency, this is set to (at least) the maximum frequency the network is required to operate at. :

\omega_0 = \frac = \frac

There is one remaining degree of freedom that the designer can use to maximally linearise the phase/frequency response. This parameter is usually stated as the L/C ratio. As stated above, it is not practical to linearise the phase response above 180°, i.e. half a cycle, so once a maximum frequency of operation, ''f''_m is chosen, this sets the maximum delay that can be designed in to the circuit and is given by, :

T_ = \frac

For broadcast sound purposes, 15 kHz is often chosen as the maximum usable frequency on landlines. A delay equaliser designed to this specification can, therefore, insert a delay of 33μs. In reality, the differential delay that might be required to equalise may be many hundreds of microseconds. A chain of many sections in tandem will be required. For television purposes, a maximum frequency of 6 MHz might be chosen, which corresponds to a delay of 83ns. Again, many sections may be required to fully equalise. In general, much greater attention is paid to the routing and exact length of television cables because many more equaliser sections are required to remove the same delay difference as compared to audio.

Superconductor planar implementation

Losses in the circuit cause the maximum delay to be reduced, a problem that can be ameliorated with the use of

high-temperature superconductors High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previou ...

. Such a circuit has been realised as a

lumped-element The lumped-element model (also called lumped-parameter model, or lumped-component model) simplifies the description of the behaviour of spatially distributed physical systems, such as electrical circuits, into a topology consisting of discrete e ...

planar implementation in

thin-film A thin film is a layer of material ranging from fractions of a nanometer ( monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many a ...

using

microstrip Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as the substrate. Microstrip lines are used to convey microwave-freque ...

technology. The traces are the superconductor

yttrium barium copper oxide Yttrium barium copper oxide (YBCO) is a family of crystalline chemical compounds that display high-temperature superconductivity; it includes the first material ever discovered to become superconducting above the boiling point of liquid nitrogen ( ...

and the substrate is

lanthanum aluminate Lanthanum aluminate is an inorganic compound with the formula LaAlO3, often abbreviated as LAO. It is an optically transparent ceramic oxide with a distorted perovskite structure. Properties Crystalline LaAlO3 has a relatively high relative di ...

. The circuit is for use in the

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequency, frequencies between 300 MHz and 300 GHz respectively. Different sources define different fre ...

band and has a centre frequency of approximately 2.8 GHz and achieves a peak

group delay In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifier, ...

of 0.7 ns. The device operates at a temperature of 77 K. The layout of the components corresponds to the layout shown in the circuit diagram at the head of this article, except that the relative positions of L' and C' have been interchanged so that C' can be implemented as a capacitance to ground. One plate of this capacitor is the ground plane and it thus has a much simpler pattern (a simple rectangle) than the pattern of C which needs to be a series capacitor in the main transmission line.Chaloupka & Kolesov, p. 234

References

Cited references

* H. J. Chaloupka, S. Kolesov, "Design of lumped-element 2D RF devices", H. Weinstock, Martin Nisenoff (eds), ''Microwave Superconductivity'', Springer, 2012 .

General references

* Jay C. Adrick, "Analog television transmitters", in, Edmund A. Williams (editor-in-chief), ''National Association of Broadcasters Engineering Handbook'', 10th edition, pp. 1483-1484, Taylor & Francis, 2013 . * Phillip R. Geffe, "LC filter design", in, John Taylor, Qiuting Huang (eds), ''CRC Handbook of Electrical Filters'', pp. 76-77, CRC Press, 1997 {{ISBN, 0849389518. Linear filters Image impedance filters Analog circuits Electronic design Electronic filter topology