RF Communication systems in microwave engineering

RF Communication systems

1. RF Communication Circuits Lecture : S- Parameters

2. Impedance and Admittance matrices Impedance matrix Admittance matrix For n ports network we can relate the voltages and currents by impedance and admittance matrices where

3. Reciprocal and Lossless Networks Reciprocal networks usually contain nonreciprocal media such as ferrites or plasma, or active devices. We can show that the impedance and admittance matrices are symmetrical, so that. Lossless networks can be shown that Z ij or Y ij are imaginary Refer to text book Pozar pg193-195

4. Example Find the Z parameters of the two-port T –network as shown below Solution V 1 V 2 I 1 I 2 Port 2 open-circuited Port 1 open-circuited Similarly we can show that This is an example of reciprocal network!!

5. S-parameters Microwave device Port 1 Port 2 V i1 V r1 V t2 V i2 V r2 V t1 Transmission and reflection coefficients Input signal reflected signal transmitted signal

6. S-parameters Voltage of traveling wave away from port 1 is Voltage of Reflected wave From port 1 Voltage of Transmitted wave From port 2 Voltage of transmitted wave away from port 2 is Let V b1 = b 1 , V i1 =a 1 , V i2 =a 2 , Then we can rewrite

7. S-parameters Hence In matrix form S-matrix S 11 and S 22 are a measure of reflected signal at port 1 and port 2 respectively S 21 is a measure of gain or loss of a signal from port 1 to port 2. S12 ia a measure of gain or loss of a signal from port 2 to port 1. Logarithmic form S 11 =20 log( r 1 ) S 22 =20 log( r 2 ) S 12 =20 log( t 12 ) S 21 =20 log( t 21 )

8. S-parameters V r2 =0 means port 2 is matched V r1 =0 means port 1 is matched

9. Multi-port network network Port 1 Port 2 Port 3 Port 4 Port 5

10. Example Below is a matched 3 dB attenuator. Find the S-parameter of the circuit. Solution Z 1 =Z 2 = 8.56 W and Z 3 = 141.8 W By assuming the output port is terminated by Z o = 50 W , then Because of symmetry , then S 22 =0

11. Continue From the fact that S 11 =S 22 =0 , we know that V r1 =0 when port 2 is matched, and that V i2 =0. Therefore V i1 = V 1 and V t2 =V2 V 1 V 2 Therefore S 12 = S 21 = 0.707 V o

12. Lossless network For lossless n-network , total input power = total output power. Thus Where a and b are the amplitude of the signal Putting in matrix form a t a * = b t b * =a t S t S * a * Thus a t (I – S t S * )a * =0 This implies that S t S * =I Note that b t =a t S t and b * =S * a * In summation form Called unitary matrix

13. Conversion of Z to S and S to Z where

14. Reciprocal and symmetrical network For reciprocal network Since the [U] is diagonal , thus Since [Z] is symmetry Thus it can be shown that

15. Example A certain two-port network is measured and the following scattering matrix is obtained: From the data , determine whether the network is reciprocal or lossless. If a short circuit is placed on port 2, what will be the resulting return loss at port 1? Solution Since [S] is symmetry, the network is reciprocal. To be lossless, the S parameters must satisfy |S 11 | 2 + |S 12 | 2 = (0.1) 2 + (0.8) 2 = 0.65 Since the summation is not equal to 1, thus it is not a lossless network. For i=j

16. continue Reflected power at port 1 when port 2 is shorted can be calculated as follow and the fact that a 2 = -b 2 for port 2 being short circuited, thus b 1 =S 11 a 1 + S 12 a 2 = S 11 a 1 - S 12 b 2 b 2 =S 21 a 1 + S 22 a 2 = S 21 a 1 - S 22 b 2 (1) (2) From (2) we have a 2 -a 2 =b 2 Short at port 2 Dividing (1) by a 1 and substitute the result in (3) ,we have (3) Return loss