1. Field of the Invention
This invention relates to a technique for implementing a dispersive group delay line for the electromagnetic signal.
2. Description of the Related Art
Group delay has been a subject of interest in electromagnetic communications, wherein the transmission paths are required to have flat group delay in the pass-bands. For example, a band-pass filter based on conventional Chebyshev, Butterworth or elliptic method has a flat group delay in the pass-band and it has larger group delay near the edges of the pass-band. However, the larger group delay response outside of the pass-band is of no particular consequence in most cases. As a result, most of efforts focused on the flat group delay in the microwave components study. Unfortunately, electromagnetic communication channels suffer strong group delay variation in air or other transmission paths and the time domain waveforms become distorted when impulse signals are considered. The group delay line can be used to minimize the distortion effect.
Dispersive delay lines using conventional all-pass technology experience small group delay time. A cascade connection of all-pass delay units improves the overall response in the sense of obtaining larger group delay time. However, it increases the circuit area as well as transmission losses. Although surface acoustic wave devices are compact and provide large delays, their applications are limited to low-frequency and narrow-bandwidth applications. Therefore, there is a need for a technique for implementing a group delay line with larger frequency-sensitive delay time, low-loss response for wide-bandwidth applications.
Briefly, in accordance with the invention, a group-delay network is provided for tuning the propagation delay time of designated signal frequencies from a source to an output load. The basic cell of the group delay device comprises a main transmission path that is connected to the source and the output at two ends of the transmission path, a couple of pairs of unequal-length, parallel, open stubs, a couple of pairs of complementary slot lines. The pairs of unequal-length, parallel stubs are directly connected to the main transmission path, wherein one pair of stubs are different from another pair of stubs in the sense of electric length θi (i=1, 2). In other words, two electric (and physical) lengths of stubs are different from each other, as shown in
Z1b cot θ1+Z2b cot θ2=0. (1)
The maximum group delay Gd in the pass-band is
where T0 is the propagation delay time for the signal traveling across one of unequal-length stubs, and δ0 is the normalized bandwidth of the pass-band.
In a preferred embodiment, the group delay is determined by the propagation delay time of each one of the unequal-length stubs, the normalized pass-band band-width and characteristic impedances of both main transmission path and unequal-length stubs.
In applications where group delays of certain bands of high-frequency signals are to be tuned, the present invention can be realized on a printed circuit board. For the main transmission path and two pairs of unequal-length, parallel stubs, each element is fabricated in changing the conductor strip width and length of the element. For the complementary slot line, the conductor is removed from the ground conductor plane to form the strip-like non-conductor strip. The complementary slot line is placed just beneath the corresponding stub, and the stub is separated from the complementary slot line with the insulating dielectric substrate.
To appreciate the details of the present invention, as shown in
The input impedance Zin,i looking from the main line Z0 toward each of the open stub is
Zin,i=jZi cot(βiblib), (i=1,2). (3)
When one of the physical lengths lib is equal to a quarter guided wavelength, the input impedance Zin,i is zero. As a result, a transmission zero occurs. When the open stub is smaller than a quarter guided wave-length, the open stub appears to be capacitive. On the other hand, if the open stub is larger than a quarter guided wave-length, it is inductive. When two parallel stubs with different physical lengths are implemented, two transmission zeros occur at two respective frequencies. At a frequency located between two transmission-zero frequencies, one Zin,i (i=1,2) is inductive and another is capacitive. When Zin,1+Zin,2=0, the total input impedance due to two parallel stubs is infinite, and a total transmission through the main line occurs. As a result, a pass-band is provided between two transmission nulls. The pass-band exhibits excessive group delay.
For the circuit shown in
Substituting both (3) and (5) into (4), we obtain the transmission coefficient S21
where θiβiblib (i=1,2).
The complex scattering parameter S21 can be expressed in the polar form as S21=|S21|∠S21. ∠S21 is the argument of S21 and it is given as follows
As stated above, a pass-band is lying between two transmission nulls caused by parallel stubs. The group delay Gd of the basic cell is defined as
where ω is the angular frequency of signal. The group delay Gd is determined by characteristic impedance Zib(i=1,2), and electrical length θi of transmission lines. Upon the substitution of (7) into (8), we obtain
T1 and T2 in (9a) and (9b) are propagation delay time for signal traveling across lines l1b and l2b, respectively, i.e., dθi/dω=Ti (i=1,2). The maximum group delay occurs at the total transmission frequency. Substituting Z1b cot θ1+Z2b cot θ2=0 into (9), to obtain
To extract the physical insight regarding the maximum group delay of this dispersive transmission line, we further simplify its mathematical expressions. A transmission-zero frequency occurs when the physical length of a stub is a quarter guided wavelength. The electrical lengths of two stubs at the total-transmission frequency of the pass-band can thus be set as follows
θ1=π/2−δ1, θ2=π/2+δ2. (11)
δi (i=1,2) is the electrical length distance in radian between the electrical length at the total transmission frequency of the pass-band and the electrical length at the transmission null frequency caused by the respective stub. If it is assumed that δ1=δ2=δ, (10) is further simplified to the following
For narrow pass-band tan δ≅δ and an 2δ<<1. Under such a condition, the group delay Gd in (12) now becomes as follows
Notice that Ti (i=1, 2) is the propagation delay time for the signal traveling across the stub line. If we assume that δ1=δ2=δ0/2 and T1=T2=T0, (13) can be simplified further to the following
where T0 is the propagation delay time across a quarter guided wavelength and δ0 is the normalized bandwidth between two transmission nulls caused by two stubs.
As shown in
The introduction of complementary slot lines is to transform the induced, band-limited pass-band to an all pass-band, which is |S21|=1. L1t and L2t in
The three-dimension schematic drawing of basic cell of a group delay line in
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Number | Date | Country | |
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20150200438 A1 | Jul 2015 | US |