Summary of Lecture (5).pptxMicrowave engineering is a specialized field within electrical and electronics engineering that focuses on the study, design, and application of devices and systems utilizing electromagnetic waves at microwave frequencies

Microwave engineering is a specialized field within electrical and electronics engineering that focuses on the study, design, and application of devices and systems utilizing electromagnetic waves at microwave frequencies. It involves the analysis and design of circuits, components, and systems, finding applications in telecommunications, radar, navigation (like GPS), medical imaging (MRI), remote sensing, and consumer electronics

1. CHAPTER SEVEN: IMPEDANCE TRANSFORMATION & MATCHING

2. 7.1 OVERVIEW One of the most critical requirements in designing RF Ccts is that, the maximum possible signal energy is transferred at each point. The signal should propagate in a forward direction with a negligible echo (ideally, zero). Echo signal not only reduces the power available but also deteriorates the signal quality due to the presence of multiple reflections. The Signal Energy in impedance form can be transformed to a new value by adjusting the turns ratio of a transformer (please refresh your memory on Impedance Transformers) that couples it with the circuit. These Circuits Include TL Stubs, Resistive & Reactive Networks.

3. Impedance-matching Networks Are Employed At The Input And Output Of An Amplifier Circuit. These Networks May Also Be Needed To Perform Other Tasks, Such As: Filtering The Signal & Blocking Or Passing The Dc Bias Voltages. Block Diagram Of An Amplifier Circuit

4. 7.1: I MPEDANCE TRANSFORMATION An impedance transformation network is a two-port network that when connected in series with an impedance ZL at one port, will result in Zs being seen on another port. • ZL is usually not equal to Zs (otherwise there will be no need for transformation ). Zs is known as the image impedance of ZL . We immediately notice that the transformation network is a 2-port network. Maximum power is delivered when load is matched to the TL ( assuming generator is matched ). Please kindly read more on from the attached PDF File on Impedance Transformation.

5. Impedance Matching Impedance Matching Is Very Desirable With RF TL. Standing Waves Lead To Increased Losses & Frequently Cause The Transmitter To Malfunction. A Line Terminated In Its Zo Has A Standing-wave Ratio Of Unity & Transmits A Given Power Without Reflection. Also, Tx Efficiency Is Optimum Where There Is No Reflected Power. A "Flat" Line Is Non-resonant; That Is, Its Zin Always Remains At The Same Value Zo When The Freq Changes.

6. At microwave frequencies the measurement of voltage or current is difficult (or impossible), Unless a clearly defined terminal pair is available. Such a terminal pair may be present in the case of TEM-type lines (such as coaxial cable, microstrip line, or stripline ), But does not strictly exist for non-TEM lines (such as rectangular, circular, or surface waveguides).

7. Matching: A TL Has A Special Meaning, One Differing From That Used In Circuit Theory To Indicate Equal Impedance Seen Looking Both Directions From A Given Terminal Pair For Maximum Power Transfer. In Circuit Theory, Maximum Power Transfer Requires The Load Impedance To Be Equal To The Complex Conjugate Of The Generator. This Condition Is Sometimes Referred To As A Conjugate Match. In TL Problems Matching Means Simply Terminating The Line In Its Zo .

8. A common appln of RF TLs is a feeder connection b/n a transmitter & an antenna. Usually the Zin to the antenna itself is not equal to the Zo of the line . The Zout of the Tx’tter may not be equal to the Zo of the line. Thus, Matching devices are necessary to flatten the line. A complete matched TL system is shown

9. For a low-loss or lossless TL at RF, the Zo of the line is resistive. At every point the impedances looking in opposite directions are conjugate. If Zo is real, it is its own conjugate. Matching can be tried first on the load side to flatten the line; then adjustment may be made on the Tx’itter side to provide maximum power transfer. At audio freqs an iron-cored transformer is almost universally used as an impedance-matching device.

10. Occasionally an iron-cored transformer is also used at RF. In a practical transmission-line system, the transmitter is ordinarily matched to the coaxial cable for maximum power transfer. Because of the variable loads, however, an impedance-matching technique is often required at the load side . Since the matching problems involve parallel connections on the TL, It is necessary to work out the problems with admittances rather than impedances . The Smith chart itself can be used as a computer: To convert the normalized impedance to admittance by a rotation of 180°, as described earlier.

11. 7.2 Impedance Measurements At Mw freqs , the measurement of voltage or current is difficult (or impossible ), Unless a clearly defined terminal pair is available. Such a terminal pair may be present in the case of TEM-type lines (such as coaxial cable, microstrip line, or stripline ), But does not strictly exist for non-TEM lines (such as rectangular, circular, or surface waveguides ).

12. To find the impedance, we need to measure at least two values because impedance is a complex quantity. Many modern impedance measuring instruments measure the real & the imaginary parts of an impedance vector & then convert them into the desired parameters such as: | Z |, θ, | Y|, R , X , G , B , C , and L . It is only necessary to connect the unknown component, circuit, or material to the instrument. Measurement ranges and accuracy for a variety of impedance parameters are determined from those specified for impedance measurement.

13. Automated measurement instruments allow you to make a measurement by merely connecting the unknown component, circuit, or material to the instrument. However , sometimes the instrument will display an unexpected result (too high or too low.) One possible cause of this problem is incorrect measurement technique, or the natural behaviour of the unknown device.

14. Measurement Methods There are many measurement methods to choose from when measuring impedance, each of which has advantages and disadvantages. One must consider measurement requirements & conditions before choosing the most appropriate method, While considering such factors as: Freq Coverage, Measurement Range, Measurement Accuracy, & Ease Of Operation. Each choice will require some tradeoffs : As there is not a single measurement method that includes all measurement capabilities.

15. RF I-V Impedance Measurement up to the microwave region.

16. 7.3 Single-stub Matching What Is A When a lossless transmission line is terminated by an impedance ZL , The magnitude of the reflection coefficient (the VSWR) on it remains constant , But its phase angle can be anywhere between +180◦ & −180◦. It represents a circle on a Smith chart, and a point on this circle represents the normalized load. As one moves away from the load, the impedance ( or the admittance) value changes. This movement is clockwise on the VSWR circle .

17. The real part of the normalized impedance (or normalized admittance) becomes unity at certain points on the line. Addition of a single reactive element or a TLs stub at this point can eliminate the echo signal and reduce the VSWR to unity beyond this point . A finite-length TL with its other end an open or short circuit is called a stub and behaves like a reactive element. Two different possibilities of determining the location on a lossless n feeding line where a stub or a reactive element can be connected to eliminate the echo signal are: A Series Or A Shunt Element

18. Although single-lumped inductors or capacitors can match the TLs, it is more common to use the susceptive properties of short-circuited sections of transmission lines. Short-circuited sections are preferable to open-circuited ones because a good short circuit is easier to obtain than a good open circuit. Although single-lumped inductors or capacitors can match the transmission line, it is more common to use the susceptive properties of short-circuited sections of TL. Short-circuited sections are preferable to open-circuited ones because a good short circuit is easier to obtain than a good open circuit.

19. For a loss less line with Yg = Yo , maximum power transfer requires Y11 = Yo , where Y11 is the total admittance of the line and stub looking to the right at point 1-1 in diagram below. The stub must be located at that point on the line where the real part of the admittance, looking towards the load, is Yo . In a normalized unit Y11 must if the stub has the same characteristic impedance as that of the line. Otherwise The stub length is then adjusted so that its susceptance just cancels out the susceptance of the line at the junction.

20. Single-stub Matching

21. 7.4 Double-stub Matching Since single-stub matching is sometimes impractical because the stub cannot be placed physically in the ideal location, d ouble-stub matching is needed. Double-stub devices consist of two short-circuited stubs connected in parallel with a fixed length b/n them. The length of the fixed section is usually: one-eighth , three-eighths, or five-eighths of a wavelength. The stub that is nearest the load is used to adjust the susceptance , L ocated at a fixed wavelength from the constant conductance unity circle (g = 1) On an appropriate constant-SWR circle.

22. Then the admittance of the line at the second stub is: In these two equations, It is assumed that the stubs and the main line have the same characteristic admittance. If the positions and lengths of the stubs are chosen properly , There will be no standing wave on the line to the left of the second stub measured from the load.

23. Double-stub Matching

24. Normally the solution of a double-stub-matching problem can be worked out backward from the load toward the generator, Since the load is known & the distance of the first stub away from the load can be arbitrarily chosen. In quite a few practical matching problems, however, Some stubs have a different Zo from that of the line, The length of a stub may be fixed, and so on. So it is hard to describe a definite procedure for solving the double-matching problems.

25. 7.5 Matching with Lumped Elements Network analysis assumes that the physical dimensions of the network are much smaller than the electrical wavelength, While TLs may be a considerable fraction of a wavelength, or many wavelengths, in size. Thus a TL is a distributed parameter network , where voltages and currents can vary in magnitude and phase over its length, While ordinary Network analysis deals with lumped elements , where voltage & current do not vary appreciably over the physical dimension of the elements. A TL is often schematically represented as a two-wire line it always have at least two conductors.

26. The piece of line of infinitesimal length _z can be modeled as a lumped-element circuit, as shown below: Where: R , L , G , and C are per-unit-length quantities defined as follows: R = series resistance per unit length, for both conductors, in _ /m. L = series inductance per unit length, for both conductors, in H/m. G = shunt conductance per unit length, in S/m. C = shunt capacitance per unit length, in F/m.

27. Voltage and current definitions and equivalent circuit for an incremental length of TL. ( a) Voltage and current definitions. ( b) Lumped-element equivalent cct .

28. END OF CHAPTER 7