Abstract:
A basic cell of a microwave group delay line is disclosed for tuning the electromagnetic signal propagation delay time from signal source ( 1 ) to output ( 5 ), wherein two pairs of unequal-length stubs ((L 1b , L 1b ), (L 2b , L 2b )) are placed on both sides of the main transmission path ( 2 ) in the signal layer and two pairs of complementary slot-lines ((L 1t , L 1t ), (L 2t , L 2t )) are placed on both sides of the main transmission path ( 2 ) in ground plane for microstrip structure. Unequal-length stubs are placed in central layer and complementary slot-lines are placed in either outer conductor ground planes for strip-line structure. The characteristic impedances (Z 0 , 2Z 1b , 2Z 2b , 2Z 1t , 2Z 2t ) of transmission paths are selected to control group delay time and minimize reflection of signals from signal source to output. A cascade connection of the basic cell forms a delay line system.

Description:
BACKGROUND OF THE INVENTION 
     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. 
     SUMMARY OF THE INVENTION 
     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 θ i  (i=1, 2). In other words, two electric (and physical) lengths of stubs are different from each other, as shown in  FIG. 1 , and θ 1 ≠θ 2 . The pair of stubs (2Z 1b , 2Z 1b ) is referred to as unequal in length to the pair of stubs (2Z 2b , 2Z 2b ), which are also shown in  FIGS. 2 and 4 . Two pairs of complementary slot lines are corresponding to the characteristics of two pairs of unequal-length, open stubs, respectively, which are omitted in  FIG. 1 . Z S  and Z L  in  FIG. 1  are source and load impedances and ( 1 ) and ( 5 ) are surface end and output load, respectively, and Z 0  is the impedance of a main line, which is also shown in  FIG. 2 . Two pairs of unequal-length, parallel stubs are employed to generate a pass-band lying between two stop-bands. The maximum transmission coefficient in the pass-band, which is bounded by two transmission nulls in the frequency band, is determined by the following relationship
 
 Z   1b  cot θ 1   +Z   2b  cot θ 2 =0.  (1)
 
The maximum group delay G d  in the pass-band is
 
                       G   d     ≈     2   ⁢           ⁢     T   o     ⁢       Z   o         Z     1   ⁢           ⁢   b       ⁢       Z     2   ⁢           ⁢   b       /     (       Z     1   ⁢           ⁢   b       +     Z     2   ⁢           ⁢   b         )           ⁢     1     δ   o   2           ,           (   2   )               
where T 0  is the propagation delay time for the signal traveling across one of unequal-length stubs, and δ 0  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. 
    
    
     
       BRIEF SUMMARY OF THE DRAWINGS 
         FIG. 1  shows the equivalent transmission line representation of the basic cell of a group delay line. 
         FIG. 2  shows a schematic drawing of unequal-length stubs of basic cell in the top signal layer. 
         FIG. 3  shows a schematic drawing of unequal-length complementary slot lines of basic cell in the bottom ground layer. 
         FIG. 4  shows a three-dimension schematic drawing of basic cell of a group delay line. 
         FIG. 5  shows the cascade connection of basic cells of the group delay line network in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     To appreciate the details of the present invention, as shown in  FIGS. 2-5 , a general understanding of transmission lines will prove helpful. In this regard, reference should be made to  FIG. 1  for the basic cell of the group delay line, where (the drawing is a conventional, prior to art transmission line,) 2Z ib  (i=1, 2) is the characteristic impedance, β ib  is the propagation constant, and l ib  is the physical length of transmission line. The electric lengths of open stubs 2Z 1b  and 2Z 2b  are unequal, i.e., θ 1 =β 1b l 1b ≠β 2b l 2b =θ 2 , or l 1b ≠l 2b  when β 1b =β 2b . The lengths L 1b  and L 2b  in  FIG. 2  are used to represent l 1b  and l 2b , respectively. In the following discussion, the equivalent characteristic impedance of parallel stubs (2Z ib , 2Z ib ) is changed to Z ib  so as to simplify the mathematical representation. Referring to  FIGS. 1 to 5 , a group delay network is depicted. The group delay network connects a source end (the element Z S  of  FIG. 1  and the signal source end  1  of  FIG. 4 ) and an output load end (the element Z L  of  FIG. 1  and the load end  5  of  FIG. 4 ). In this embodiment, the microstrip structure of the invention includes a main signal transmission path  2  ( FIG. 4 ), a source end  1  ( FIG. 4 ), an output load  5  ( FIG. 4 ), a signal layer  11  ( FIGS. 2, 4 ), an insulating layer  12  ( FIGS. 2, 4 ), a ground layer  13  ( FIGS. 3, 4 ), slot lines  131  ( FIGS. 3, 4 ), and main line Z 0 . The group delay device includes the main signal transmission path  2  for the input signal and output signal, two pairs of unequal-length, open stubs ((L 1b , L 1b ), (L 2b , L 2b )) placed on two sides of the main signal transmission path  2  ( FIGS. 1, 2, 4 ), two pairs of unequal-length, complementary slot lines ((L 1t , L 1t ), (L 2t , L 2t )) that are placed in the ground plane of the microstrip structure, as shown in  FIGS. 3, 4 . As shown in  FIGS. 2, 3, and 4 , each of the open stubs ((L 1b , L 1b ), (L 2b , L 2b )) and each of the complementary slot lines ((L 1t , L 1t ), (L 2t , L 2t )) has a parallel portion and a non-parallel portion. Each parallel portion of the open stubs ((L 1b , L 1b ), (L 2b , L 2b )) and the complementary slot lines ((L 1t , L 1t ), (L 2t , L 2t )) has an unequal-length. Each non-parallel portion of the open stubs ((L 1b , L 1b ), (L 2b , L 2b )) and the complementary slot lines ((L 1t , L 1t ), (L 2t , L 2t )) cross and are connected at a same location. Each open stub is uniform, non-uniform or meandered along the line and each complementary slot line is uniform, non-uniform or meandered. Each of the open stubs ((L 1b , L 1b ), (L 2b , L 2b )) located on the insulating layer  12  corresponds to one of the complementary slot lines ((L 1t , L 1t ), (L 2t , L 2t )) located on ground layer  13  forming a multiple layer structure. 
     The input impedance Z in,i  looking from the main line Z 0  toward each of the open stub is
 
 Z   in,i   =jZ   i  cot(β ib   l   ib ), ( i= 1,2).  (3)
 
When one of the physical lengths l ib  is equal to a quarter guided wavelength, the input impedance Z in,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 Z in,i  (i=1,2) is inductive and another is capacitive. When Z in,1 +Z in,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  FIG. 1 , the scattering parameter S 21  (or transmission coefficient) is as follows 
                       S   21     =     [       2   ⁢           ⁢     Z   in           Z   in     +     Z   o         ]       ,     
     ⁢   where           (   4   )                 Z   in     =       [     1       1     Z   o       +     1     Z     in   ,   1         +     1     Z     in   ,   2             ]     .             (   5   )               
Substituting both (3) and (5) into (4), we obtain the transmission coefficient S 21 
 
                       S   21     =     1     1   +     j   ⁢         Z   o     ⁡     (         Z     1   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   1       +       Z     2   ⁢           ⁢   b       ⁢     θ   2         )         2   ⁢           ⁢     Z     1   ⁢           ⁢   b       ⁢     Z     2   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   1     ⁢   cot   ⁢           ⁢     θ   2                 ,           (   6   )               
where θ i β ib l ib  (i=1,2).
 
     The complex scattering parameter S 21  can be expressed in the polar form as S 21 =|S 21 |∠S 21 . ∠S 21  is the argument of S 21  and it is given as follows 
                     ∠S   21     =       -   Π     -         tan     -   1       ⁡     [         Z   o     ⁡     (         Z     1   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   1       +       Z     2   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   2         )         2   ⁢           ⁢     Z     1   ⁢           ⁢   b       ⁢     Z     2   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   1     ⁢   cot   ⁢           ⁢     θ   2         ]       .               (   7   )               
As stated above, a pass-band is lying between two transmission nulls caused by parallel stubs. The group delay G d  of the basic cell is defined as
 
                       G   d     =     -       ⅆ     ∠S   21         ⅆ   ϖ           ,           (   8   )               
where ω is the angular frequency of signal. The group delay G d  is determined by characteristic impedance Z ib (i=1,2), and electrical length θ i  of transmission lines. Upon the substitution of (7) into (8), we obtain
 
                           ⁢         G   d     =         Z   o     ⁢     Z     1   ⁢           ⁢   b       ⁢     Z     2   ⁢           ⁢   b       ⁢     {     A   -   B     }           2   ⁢           ⁢     Z     1   ⁢           ⁢   b     2     ⁢     Z     2   ⁢           ⁢   b     2     ⁢     cot   2     ⁢     θ   1     ⁢     cot   2     ⁢     θ   2       +     2   ⁢           ⁢         Z   o   2     ⁡     (         Z     1   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   1       +       Z     2   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   2         )       2             ,     
     ⁢           ⁢   where             (   9   )                   A   =         (         Z     1   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   1       +       Z     2   ⁢           ⁢   b       ⁢   cot   ⁢           ⁢     θ   2         )     [           ⁢         (       cot   ⁢           ⁢     θ   2       +       cot   2     ⁢     θ   1     ⁢   cot   ⁢           ⁢     θ   2         )     ⁢     T   1       +     cot   ⁢           ⁢     θ   1       +       cot   2     ⁢     θ   2     ⁢   cot   ⁢           ⁢     θ   1         )     ⁢     T   2         ]     ,     
     ⁢           ⁢   and           (     9   ⁢   a     )                       ⁢     B   =       (         Z     1   ⁢           ⁢   b       ⁢     T   1       +       T     2   ⁢           ⁢   b       ⁢     T   2       +       T     1   ⁢           ⁢   b       ⁢     T   1     ⁢     cot   2     ⁢     θ   1       +       Z     2   ⁢           ⁢   b       ⁢     T   2     ⁢     cot   2     ⁢     θ   2         )     ⁢   cot   ⁢           ⁢     θ   1     ⁢   cot   ⁢           ⁢       θ   2     .                 (     9   ⁢   b     )               
T 1  and T 2  in (9a) and (9b) are propagation delay time for signal traveling across lines l 1b  and l 2b , respectively, i.e., dθ i /dω=T i  (i=1,2). The maximum group delay occurs at the total transmission frequency. Substituting Z 1b  cot θ 1 +Z 2b  cot θ 2 =0 into (9), to obtain
 
     
       
         
           
             
               
                 
                   
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     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
 
θ 1 =π/2−δ 1 , θ 2 =π/2+δ 2 .  (11)
 
δ i  (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 δ 1 =δ 2 =δ, (10) is further simplified to the following
 
     
       
         
           
             
               
                 
                   
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                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     For narrow pass-band tan δ≅δ and an  2 δ&lt;&lt;1. Under such a condition, the group delay G d  in (12) now becomes as follows 
                     G   d     ≈           Z   o       2   ⁢           ⁢     Z     1   ⁢           ⁢   b       ⁢     Z     2   ⁢           ⁢   b       ⁢     δ   2         ⁡     [         Z     1   ⁢           ⁢   b       ⁢     T   1       +       Z     2   ⁢           ⁢   b       ⁢     T   2         ]       .             (   13   )               
Notice that T i  (i=1, 2) is the propagation delay time for the signal traveling across the stub line. If we assume that δ 1 =δ 2 =δ 0 /2 and T 1 =T 2 =T 0 , (13) can be simplified further to the following
 
                       G     d   ,   narrowband       ≈     2   ⁢     T   o     ⁢       Z   o         Z     1   ⁢           ⁢   b       ⁢       Z     2   ⁢           ⁢   b       /     (       Z     1   ⁢           ⁢   b       +     Z     2   ⁢           ⁢   b         )           ⁢     1     δ   o   2           ,           (   14   )               
where T 0  is the propagation delay time across a quarter guided wavelength and δ 0  is the normalized bandwidth between two transmission nulls caused by two stubs.
 
     As shown in  FIG. 5 , a cascade connection of the basic cells (BasicCell-1, BasicCell-2, . . . BasicCell-N) using segments Z 0 , Z 1 , . . . , Z n-1 , Z n  (n is a positive integer) to form a group delay line system between signal and ground. 
     The introduction of complementary slot lines is to transform the induced, band-limited pass-band to an all pass-band, which is |S 21 |=1. L 1t  and L 2t  in  FIG. 3   FIGS. 3 and 4  are the lengths of complementary slot lines 2Z 1t  and 2Z 2t , respectively. 
     The three-dimension schematic drawing of basic cell of a group delay line in  FIG. 4  is a three-layers structure, where ( 11 ) is the signal (top) layer, ( 12 ) is the insulating (middle) layer, and ( 13 ) is the conductor ground (bottom) layer.