ON MICROWAVE MEASUREMENT OF S-PARAMETER USING RING HYBRID RAT-RACE CIRCUIT

T. N. C. Wang*, N.S Zhou**, P. D. H. Wang** *I,GIC Shanghai Office, **Shanghai Univ.

Abstract

Using a single ring hybrid and a cascaded double ring hybrid microwave circuits, a set of equations have been derived in terms of measured output powers at the difference or sum ports of the ring hybrid. These equations can be used straightforward to compute the reflection and transmission coefficients of a device under test. In comparison with a modem microwave network analyzer, this ring hybrid measurement method together with a set of derived equations offers a simple and very low cost technique for s- parameter measurement.

I. Introduction A microwave ring hybrid, or rat-race can be used to

measure reflection and transmission coefficients or s- parameter, of a microwave device. In comparison with the measurement of s-parameter using a modem network analyzer, this "ring hybrid method" features simplicity and very low cost. With a microwave source input at sum port or difference port of a ring hybrid circuit, one simply measures the scattered output powers fiom the other relevant ports of the ring hybrid circuit. The magnitude and phase of reflection and transmission coefficients of a device under test can be simply calculated fi-om a set of equations derived from our designed ring hybrid circuit configurations.

In the following sections, we shall describe several measurement methods using a single ring hybrid and a cascaded double ring hybrid configurations along with specific circuit connections. For the ring hybrid configurations shown in Fig.2 and Fig.3, we have done a detailed analysis and derived a set of relevant formulas in terms of measured output powers and the other given parameters for calculation of reflection and transmission coefficients.

11. Basic Characteristics Of A King Hybrid A ISO" ring hybrid, or rat-race, in microstrip line or

stripline form is shown in Fig.1. When a unit amplitude wave incident at port 1 (the sum port), at the ring junction, this wave will divide into two components which both arrive in phase at ports 2 and 3, and 180" out of phase at port 4 (the difference port). Using the even-odd mode analysis technique [ I ] , it can be shown that the amplitudes of the scattered waves (b,> i=1.2,3,4) froni the each ports of the ring hybrid are given by:

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Equation (la) shows that the input port (the sum port) is matched (i.e., no reflections), the difference port 4 is isolated, and fiom Equation (lb) the power inputed from port 1 is evenly divided in phase between ports 2 and 3. Similarly, when a unit amplitude wave incident at port 4 (the difference port), the scattered waves at each port are given by:

Eq. (2) shows that, in this case, the input port 4 is matched, port 1 is isolated, and the input power is evenly divided into ports 2 and 3, with a 180' phase difference.

The above basic scattering properties of a ring hybrid can be used to measure the reflection coefficients and transmission coefficients of microwave devices.

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Fig . I . A 180 e Ring - Hybrid

II1.On Measurement Of Reflection Coefficient

In case of using a single ring-hybrid, a device under testis connected at port 2 and a reference load with a reflection coefficient rj is connected at port 3. An input microwave source (its output impedance matched to &) of power Po is

I? Using A Single Ring-Hybrid Circuit

connected to the sum port 1. A simple arrangement of the circuit is illustrated in Fig.2. We measure scattered powers at the difference port 4 and /or the sum port 1 by setting the reference load conditions (i.e.,ri ) to determine the reflection coefficient r of the tested device. Analysis or descriptions for several approaches are given below:

A.On Measuring Scattered Power P4 At The'Difference Port

In reference to Fig.Za, scattered waves at ports 2 and 3 are given by bl = (a,+&)/*, b, = (a,-a,)/fi. Using a impedance matched power meter, a, = 0, thus we have b, = bj = a,/fi . The scattered wave at port 4 is given by b4 = (a2-a3)/ fi. But a, = b,r, a3 = b3ri, or a, = a , r / f l , a, = a l r i / f i . Substituting these relations into the expression for b,, we obtain

(3 1 b, = al(r-r-i )n .... - ............................ From Eq.(3), in terms of input power Po (Po = I a, 1 ') and measured power P4 (P4 = I b, I 2), we have P, =I a , I * I r- r, I where P, = P, /Po (power ratio). To write explicitly, we have

or , 4Pr =I r-ri I ',

4pr = I r I 2 + i ri I 2 - 2 I r I I ri I cos (4 - +,)---.-- (4)

clearly, in r-plane, the locus of Eq.(4) is a family of cycles of radius = 2 G r , centers at I ri I and . For i d 3, it is difficult to solve I r I and Q analytically from Eq.(4). However, one can easily solve graphically. By letting I r, I = 1 (i.e., let line of port 3 be open or shorted) and

making the length such that $I = 0 O , 90 O , 180 O , and measure P, for each cases. In the r-plane, we can draw three cycles that will give a unique intersect point to determine I r i and 4. Note that I r I is always less or equal than unity. If one of the intersect point fiom the first two cycles is outside the unit cycle in the ??-plane then the correct solution for r is the intersect point inside the unit cycle (In this case, only hvo measurements are sufficient).

B. On Measuring Scattered Power PI At the Sum Port

The ring-hybrid test set-up for this case is shown in Fig.2b. The scattered wave a1 port I is given by b, = (a,+a,)/fi =

(b , r+b,r , ) / f i = a , ( r - r , )i2. Similarly, we have the equation for I r I and $ below:

It is clear that the locus of Eq.(5) are cycles in the r-plane, with radius at 2 G r and centers at ( - 1 ri 1 , Qi). Graphical method to solve for r from Eq.(5) is similar to that discussed above.

C. On Analvtical Solutions

(1) Single Port Measurement For Four Separate Phases Of Reference Load (&, i = I ,2,3,4).

We measure four times of the scattered power P4 at the difference port by setting four phase values $i, i = 1,2,3,4, and keeping I ri I= constant (usually I rii= 1). Using Eq.(4), we can deduce:

$ = arctan ([M(cos $I - cos Q3 ) - (cos $, - cos $I,)]/

[M(sin $I -sin 4 1 ~ ) -(sin Q4 -sin Q 2 ) J ) - - - * - . - * - ( 5 ) where M = (P,., - P4,2)/ (P4.1 - P4J

If one adjust the line lengths of port 3 such that $, be sequentially $I = O0,& = 90°, & = 180" and 9, = 270°, then Eq.(5) simplifies to Q = arctan (M). After calculated Q from Eq.(5), one can substitute Q back to Eq.(4) and solve for I r I .

(2).Two Ports (Sum Port And Difference Port) Measure- ment For Two Separate Phases Of r,

In this case, we measure the scattered powers fkom the sum and difference ports for two cases of reference load, i.e., ir, I , $ I and lr21, $?. We then have the following four equations

From Eq.(6), one can solve for $ given by

$ = arctan [(Mcos $, - cos Q2)/(sin $: - Msin$, )I, where M = (PI,,- P,,,)/ (PI, , - P,,,)--..-.-...-...-.-. (7)

If $, = O0&= 90°, then Q is simply given by Q = arctan (M). After obtaining $, I r I , I r, I , and I TI i can be solved from Eq.(6). If we set I r, I = I r2 I = 1: then the solution of I r I can be taken as the average of the solutions fiom the four equations of Eq.(6).

@).Two Ports (Sum Port And Difference Port ) Measure- ment For A Single Case Of r; = r, .

I n this case, Eq.(6) reduces to Eqs.(6a) and (6b). From these two Equations, we obtain

Since Po and rl (i.e., I 1', I , 4, ) are known, P; I . P, , , &e measured values, 1 r I and Q can be simply calculated from Eq.(8).

(4).Single Port (The Difference Port) Measurement For A

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Single Case Of ri = r, In this case, we let rl = I/$, , Eq.(6) reduces to 4P.8'0 = 1 r 1' + I -2 I r I cos (4 - $,).We can adjust of the reference load such that 4 - 4, = 180" to obtain maximum value of P4, i.e., 4P4..,/P0 = N = ( 1 r I + I)'. On the other hand, when 4, is such that I$ - 4, 4, Measured P, becomes a minimum, i.e., 4P4,,/Po =.n = ( I r I - 1)'. Thus, 1 r I is given by I r I = (6 - \6)/2 , and the phase angle 4 is given by (I = (180"- - (I,." )/2.

Fig.2a. One Port Measurement

Fig.2b.Tbm Port Measurement Fig. 2. Single Ring-Iiyhrid C i r c u i t

IV. On Measurement Of Reflection And Transmission Coefficients Using Double Ring - Hybrid Circuits.

A.Measurement Of Reflection Coefficient r = i r I /I$.

A simple double ring-hybrid circuit set-up is shown in Fig.3a. Note that no reference load is required. The impedance of the hvo microwave power meters at the nvo difference ports of the ring-hybrids H I and H2 should be matched so that the reflected waves a, = a2 =O. With an input power Po at the sum port of H2 and measuring the scattered powers PI and P2 ~ we can calculate the I r I and 4 of the device under test. Following the notations of the two ring-hybrid, as shown in Fig.3a. it is clear that H?2= H2, = &:\x HI,= H z 2 / f i , b = H I 2 / 6 . H I f = (a i HI, )/6 and a = b r . The scattered wave b2 at the difference port of H2 is given

by b2 = (HI+ - HI2 )/6. Using the above relations, we can show that b2 = a,r/4. Note that P2 =I b2 I 2 , Po= I a, 1 * . Thus the magnetitude of reflection coefficient is given by

r I = 4 m 2 0 .............................. (9a)

The scattered wave at the difference port of H , is given by bl= (HZ1 - a ) / C After some algebra, bl= a, (6- 19/26. In terms of PI = I b, I ', P,, Po and using relation of (9a), we can show that

B.Measurement Of Transmission Coefficient S, ( I S I ,Y )

The circuit set-up is shown in Fig.3b. It is noted that this measurement is only valid for the case SI, = S2,= S = I S I /Y . Following the notations indicated in Fig.3b, we have H2' =-H2, = q/fi, a,= b , r l , H I 1 = qlfi = b, r , /&, Hlz= aJd2 = - a,/dF. Using these relations, one can show that the scattered waves at the sum port of HI. b, and at the difference port of H2, b, are given by

b, = (SH2'+H2,) /J?I= a, (S+1)/2 - * - - - * - - * . - - ( 1 oa> b2 =(SHII-H12) /$= a& (S+I)(S-1)/4 - a - ( lob)

From Eq.(lO), we can solve I S I and Y in terms of measured powers P, and P 2 , given below:

I s I = d[pl I ri I (2p1 - p0 ) + ~ P ~ P ~ ] / P ~ P , I ri I - ( I la) Y = COS" [(I ri l2Pi2- POP2) / I ri I I S I PoPI]-----(I lb)

It is seen that result of Eq.( 1 1 ) is independent of the phase angle 4i of the reference load. Usually one sets1 ri I= 1 (i.e., short or open) to simplify in measurement. It is noted, fi-om Eq.( IO), that if we make a short circuit of the two testing ports (i.e., S = O), then P2 = 0 and P, = Po . This result indicates that we can also use the circuit to measure unknown microwave source power PO.

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Fig.3a. Jieflection Coefficient M e a s u r e m e n t

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Fig. 3b. Transmissicm Coefficient Pkasura-ent

Fig.3. Double Ring Hybrid C i r c u i t

V. Concluding Remarks Using a single ring-hybrid and a cascaded double ring

hybrid circuits, we have made analysis and derived several useful expressions to calculate reflection or transmission coefficients in terms of measured, scattered power at the sum andlor the difference ports of the ring-hybrid. In microwave frequencies, ring-hybrid circuits can be simply constructed by microstrip or strip lines, with a microwave source (e.g., a VOC) and a device under test being integrated in the circuit. In comparison with a modem network analyzer, the "ring- hybrid" method described here offers a very low cost and a simple way to measure reflection and transmission coefficients with a good accuracy (since we measure powers in stead of voltage waves).

It is clear that an ideal ring-hybrid, as shown in Fig.1, is a narrow band device, with its small percentage bandwidth determined by:( 1) how good one can make the characteristic impedances (&, Z d 6 ) being a constant and (2) how good the electrical lengths between the ports of the ring-hybrid remained the same within the frequency band of interest. Thus, unlike to that of using a microwave network analyzer, measurements using the "ring-hybrid" method can only be applied to a specified frequency of interest, not to make a sweeping frequency measurement.

References: [I]. J. Reed and G.J. Wheeler, " A Method Of Analysis Of Symmetrical Four-Port Networks", IRE Trans. On Microwave Theory and Techniques, vol. MTT-4, PP. 246- 252.04.1956.

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