Lecturer Note. Lecturer-17

Transcription

1 Lecturer Note Sub: MWE Subject code: PCEC 4402 Sem: 8 th Prepared by: Mr. M. R. Jena Lecturer-17 Power dividers and directional couplers A directional coupler is a passive device which couples part of the transmission power by a known amount out through another port, often by using two transmission lines set close enough together such that energy passing through one is coupled to the other. The device has four ports: input, transmitted, coupled, and isolated. The term "main line" refers to the section between ports 1 and 2. On some directional couplers, the main line is designed for high power operation (large connectors), while the coupled port may use a small SMA connector. Often the isolated port is terminated with an internal or external matched load (typically 50 ohms). It should be pointed out that since the directional coupler is a linear device, the notations on Figure 1 are arbitrary. Any port can be the input, which will result in the directly connected port being the transmitted port, adjacent port being the coupled port, and the diagonal port being the isolated port. Physical considerations such as internal load on the isolated port will limit port operation. The coupled output from the directional coupler can be used to obtain the information (i.e., frequency and power level) on the signal without interrupting the main power flow in the system. When the power coupled out to port three is half the input power (i.e. 3 db below the input power level), the power on the main transmission line is also 3 db below the input power and equals the coupled power. Such a coupler is referred to as a 90 degree hybrid, hybrid, or 3 db coupler. The frequency range for coaxial couplers specified by manufacturers is that of the coupling arm. The main arm response is much wider (i.e. if the spec is 2-4 GHz, the main arm could operate at 1 or 5 GHz - see Figure 3). However it should be recognized that the coupled

2 response is periodic with frequency. For example, a 8/4 coupled line coupler will have responses at n8/4 where n is an odd integer. Common properties desired for all directional couplers are wide operational bandwidth, high directivity, and a good impedance match at all ports when the other ports are terminated in matched loads. These performance characteristics of hybrid or non-hybrid directional couplers are self-explanatory. Some major general characteristics are COUPLING FACTOR The coupling factor is defined as the ratio of P3 to P1 expressed in db. where P1 is the input power at port 1 and P3 is the output power from the coupled port The coupling factor represents the primary property of a directional coupler. Coupling is not constant, but varies with frequency. While different designs may reduce the variance, a perfectly flat coupler theoretically cannot be built. Directional couplers are specified in terms of the coupling accuracy at the frequency band center. For example, a 10 db coupling ± 0.5 db means that the directional coupler can have 9.5 db to 10.5 db coupling at the frequency band center. The accuracy is due to dimensional tolerances that can be held for the spacing of the two coupled lines. Another coupling specification is frequency sensitivity. A larger frequency sensitivity will allow a larger frequency band of operation. Multiple quarter-wavelength coupling sections are used to obtain wide frequency bandwidth directional couplers. Typically this type of directional coupler is designed to a frequency bandwidth ratio and a maximum coupling ripple within the frequency band. For example a typical 2:1 frequency bandwidth coupler design that produces a 10 db coupling with a ±0.1 db ripple would, using the previous accuracy specification, be said to have 9.6 ± 0.1 db to 10.4 ± 0.1 db of coupling across the frequency range. Insertion Loss- In an ideal directional coupler, the main line loss port rt 1 to port 2 (P1 - P2) due to power coupled to the coupled output port is called as insertion loss.

3 The actual directional coupler loss will be a combination of coupling loss, dielectric loss, conductor loss, and VSWR loss. Depending on the frequency range, coupling loss becomes less significant above 15 db coupling where the other losses constitute the majority of the total loss. ISOLATION Isolation of a directional coupler can be defined as the difference in signal levels in db between the input port and the isolated port when the two output ports are terminated by matched loads. Isolation can also be defined between the two output ports. In this case, one of the output ports is used as the input; the other is considered the output port while the other two ports (input and isolated) are terminated by matched loads. The isolation between the input and the isolated ports may be different from the isolation between the two output ports. For example, the isolation between ports 1 and 4 can be 30 db while the isolation between ports 2 and 3 can be a different value such as 25 db. If both isolation measurements are not available, they can assumed to be equal. If neither are available, an estimate of the isolation is the coupling plus return loss (see VSWR section). The isolation should be as high as possible. In actual couplers the isolated port is never completely isolated. Some RF power will always be present. Waveguide directional couplers will have the best isolation. If isolation is high, directional couplers are excellent for combining signals to feed a single line to a receiver for two-tone receiver tests. DIRECTIVITY Directivity is directly related to Isolation. It is defined as ratio of P4 to P3 expressed in db. where: P3 is the output power from the coupled port and P4 is the power output from the isolated port. The directivity should be as high as possible. Waveguide directional couplers will have the best directivity.

4 Directivity is not directly measurable, and is calculated from the isolation and coupling measurements as: Directivity (db) = Isolation (db) - Coupling (db) HYBRIDS The hybrid coupler, or 3 db directional coupler, in which the two outputs are of equal amplitude takes many forms. Not too long ago the quadrature (90 degree) 3 db coupler with outputs 90 degrees out of phase was what came to mind when a hybrid coupler was mentioned. Now any matched 4-port with isolated arms and equal power division is called a hybrid or hybrid coupler. Today the characterizing feature is the phase difference of the outputs. If 90 degrees, it is a 90 degree hybrid. If 180 degrees, it is a 180 degree hybrid. Even the Wilkinson power divider which has 0 degrees phase difference is actually a hybrid although the fourth arm is normally imbedded. Applications of the hybrid include monopulse comparators, mixers, power combiners, dividers, modulators, and phased array radar antenna systems. A key difference between couplers and power dividers is that couplers create a phase shift between the output signals. The main difference between directional couplers and quadrature hybrids is that directional couplers provide non-equal power splitting of the incoming signal (Fig. 3), while quadrature hybrids have equal (3 db) power splitting. Like Wilkinson power dividers, couplers are band limited and are always characterized by a low frequency (flow) and high frequency (fhigh) of operation. The main application of a directional coupler is to pick off a small portion (somewhere between 0.1% and 25%, typically) of the signal on a transmission line such that the incoming power can be actively monitored without too much loss. Since directional couplers are most often used in power sensing applications, their phase information is usually not specified. In contrast, the 90 degree phasing of quadrature hybrid couplers (Fig. 4) is always specified since the phase accuracy is critically important for many applications like IQmodulation and demodulation, single-sideband up-conversion, and image reject downconversion.

5 In both directional couplers and quadrature hybrids, the best performance is obtained when the circuits are well matched to 50. It is common for Marki Microwave couplers to obtain return loss values on the order of db, with isolations in excess of 30 db. This performance is achieved through precision coaxial-to-stripline transitions and a proprietary optimization algorithm.

6 Lecturer-18 Basic properties of dividers and couplers are three-port network (T-junction) four-port network (directional coupler) directivity measurement Different types of Power dividers and directional couplers The T-junction power divider Lossless divider, lossy divider The Wilkinson power divider Even-odd mode analysis, unequal power division divider, N-way Wilkinson divider The quadrature (90 ) hybrid branch-line coupler Coupled line directional couplers Even- and odd-mode Z0, single-section and multisection coupled line couplers The Lange coupler The 180 hybrid - rat-race hybrid, tapered coupled line hybrid Other couplers reflectometer Wilkinson power divider The Wilkinson's power divider has low VSWR at all ports and high isolation between output ports. The input and output impedances at each port is designed to be equal to the characteristic impedance of the microwave system. A typical power divider is shown in Figure 5. Ideally, input power would be divided equally between the output ports. Dividers are made up of multiple couplers, and like couplers, may be reversed and used as multiplexers.

7 The drawback is that for a four channel multiplexer, the output consists of only 1/4 the power from each, and is relatively inefficient. Lossless multiplexing can only be done with filter networks The Wilkinson power divider has these advantages: 1. It is lossless when output ports are matched. 2. Output ports are isolated. 3. It can be designed to produce arbitrary power division. Wilkinson power divider Operation- If we inject a TEM mode signal at port 1, equal in-phase signals reach points a and b. Thus, no current flows through the resistor, and equal signals emerge from port 2 and port 3. The device is thus a 3dB power divider. Port 1 will be matched if the λ/4 sections have a characteristic impedance 2Z 0. If we now inject a TEM mode signal at port 2, with matched loads placed on port 1 and on port 3, the resistor is effectively grounded at point b. Equal signals flow toward port 1, and down into the resistor, with port 2 seeing a match. Half the incident power emerges from port 1 and half is dissipated in the resistor film. Similar performance occurs when port 1 and port 2 are terminated in matched loads, and a TEM mode signal is injected at port 3. If we choose the terminal planes at 1.0 wavelengths from the three Tee junctions, the scattering matrix is Directional Coupler Directional couplers are used for coupling a light wave from one waveguide to another waveguide. By controlling the refractive index in the two waveguides, for instance by heating or current injection, it is possible to control the amount of coupling between the waveguides. Light that propagates through a dielectric waveguide has most of the power concentrated within the central core of the waveguide. Outside the waveguide core, in

8 the cladding, the electric field decays exponentially with the distance from the core. However, if you put another waveguide core close to the first waveguide, that second waveguide will perturb the mode of the first waveguide (and vice versa). Thus, instead of having two modes with the same effective index, one localized in the first waveguide and the second mode in the second waveguide, the modes and their respective effective indexes split and you get a symmetric supermode, with an effective index that is slightly larger than the effective index of the unperturbed waveguide mode, and an antisymmetric super mode, with an effective index that is slightly lower than the effective index of the unperturbed waveguide mode. Since the supermodes are the solution to the wave equation, if you excite one of them, it will propagate unperturbed through the waveguide. However, if you excite both the symmetric and the antisymmetric mode, that have different propagation constants, there will be a beating between these two waves. Thus, you will see that the power fluctuates back and forth between the two waveguides, as the waves propagate through the waveguide structure. You can adjust the length of the waveguide structure to get coupling from one waveguide to the other waveguide. By adjusting the phase difference between the fields of the two supermodes, you can decide which waveguide that initially will be excited. The directional coupler, as shown in Figure, consists of two waveguide cores embedded in a cladding material. The cladding material is GaAs, with ion-implanted GaAs for the waveguide cores. The core cross-section is square, with a side length of 3 µm. The two waveguides are separated 3 µm. The length of the waveguide structure is 2 mm. Thus, given the tiny cross-section, compared to the length, it is advantageous to use a view that don t preserve the aspect ratio for the geometry. For this kind of problem, where the propagation length is much longer than the wavelength, the Electromagnetic Waves, Beam Envelopes interface is particularly suitable, as the mesh does not need to resolve the wave on a wavelength scale, but rather the beating between the two waves.

9 The model is setup to factor out the fast phase variation that occurs in synchronism with the first mode. Mathematically, we write the total electric field as the sum of the electric fields of the two modes, The expression within the square parentheses is what will be solved for. It will have a beat length L. In the simulation, this beat length must be well resolved. Since the waveguide length is half of the beat length and the waveguide length is discretized into 20 subdivisions, the beat length will be very well resolved in the model. The model uses two numeric ports per input and exit boundary. The two ports define the lowest symmetric and antisymmetric modes of the waveguide structure.

10 Lecturer-19 Microwave Power Dividers and Couplers Power dividers and couplers are straightforward passive components. It is the attention to design detail, execution of the design, and quality of the fabrication which leads to a high performance component. Overview The splitting and recombining of electromagnetic signals is a fundamental signal processing functionality in electronics. Many circuits exist in the RF and microwave designer s toolbox to facilitate effective signal splitting and recombination. The proper choice of circuit depends on the application and requirements; many engineers become confused due to the multitude of options available. Currently, Marki Microwave offers the following types of power dividers and couplers: Resistive power dividers, Wilkinson power dividers, Directional couplers, and Quadrature Hybrid couplers. All power dividers and couplers split/combine1 electromagnetic signals. The key difference between the various circuits is how the signal is split, and more importantly, what the resultant output signals look like in terms of amplitude and phase. A. Power Dividers In most circumstances, power dividers provide equal amplitude and equal phase splitting. for both power dividers, the input signal at port 1 splits equally between output ports 2 and 3. In a resistive power divider, both output signals are 6 db lower than the input signal, and they are in phase. In Wilkinson power dividers, the output signals are 3 db below the input signal, and they are also in phase (i.e. 0 degree phase shift between the outputs). The extra 3 db of path loss in the resistive divider is caused by the extra voltage drops across the 16.7 resistors.

11 The main differences between resistive power dividers and Wilkinson power dividers are that Wilkinson power dividers have 3 db lower loss and possess the advantage of isolation between output ports (see Fig. 2). Practically speaking, Wilkinson power dividers are limited in their low frequency range (flow) to a few hundred MHz while resistive power dividers reach to DC. Coupler A key difference between couplers and power dividers is that couplers create a phase shift between the output signals. The main difference between directional couplers and quadrature hybrids is that directional couplers provide non-equal power splitting of the incoming signal, while quadrature hybrids have equal (3 db) power splitting. Like Wilkinson power dividers, couplers are band limited and are always characterized by a low frequency (flow) and high frequency (fhigh) of operation. The main application of a directional coupler is to pick off a small portion (somewhere between 0.1% and 25%, typically) of the signal on a transmission line such that the incoming power can be actively monitored without too much loss. Since directional couplers are most often used in power sensing applications, their phase information is usually not specified. In contrast, the 90 degree phasing of quadrature hybrid couplers is always specified since the phase accuracy is critically important for many applications like IQ-modulation and demodulation, single-sideband up-conversion, and image reject down-conversion. In both directional couplers and quadrature hybrids, the best performance is obtained when the circuits are well matched to 50. It is common for Marki Microwave couplers to obtain return loss values on the order of db, with isolations in excess of 30 db. This performance is achieved through precision coaxial-to-stripline transitions and a proprietary optimization algorithm. Section 2. Figures of Merit Generally, power dividers and couplers are quantified using nearly identical figures of merit, with a few subtle differences. A. Splitting Ratio/Coupling Ratio

12 Splitting ratio (a.k.a. coupling ratio) is defined as the ratio of output power to input power. By convention, the amplitude ratio is defined by the lower of the two output powers. Thus, a 90:10 split would imply a coupling ratio of 10 db and a 99:1 split would imply a coupling ratio of 20 db. Typically power dividers are designed such that the input power is equally distributed among the output ports. Thus, a 2 to 1 power divider passes 50% (-3 db) of the power to each output. A 3 to 1 power divider passes 33% (-4.8 db) of the power to each port, and so on. Directional couplers are best suited for applications requiring unequal splitting ratios. While it is theoretically possible to create Wilkinson power dividers with unequal splitting ratios (a.k.a. asymmetric Wilkinsons), it is uncommon to do so because of unrealizable fabrication tolerances. Various resistive circuits called pick-off tees, resistive taps, and resistive couplers exist that also generate unequal power splitting. Such circuits are simple voltage dividers and are similar in operation to the 6 db resistive power divider. Advantages of these circuits are size and bandwidth. Disadvantages are increased insertion loss and low isolation, which can lead to crosstalk between output channels. B. Relative Phase Shift Various power divider and coupler circuits exist which facilitate either 0 degree (in phase), 90 degree (quadrature phase), or 180 degree (differential) phase shift between the two output signals. Generally, 0o (in phase) circuits are the easiest to design, followed by the 90o and 180o circuits. Splitters that yield differential outputs are often called Magic-T s. Examples of Magic-T circuits are the rat-race coupler, the asymmetric tandem coupler, and the parallel coupled line Magic-T. Currently, Marki Microwave offers 180 degree hybrid couplers as custom designs only. Contact the factory for more information regarding these custom components. A final class of splitters exists called Baluns. Baluns are unbalanced to balanced transformers that provide a 180 degree phase shift between the two output ports. The

13 primary distinction between a Balun and a Magic-T is that Baluns are 3 port circuits that do not provide isolation between outputs. The Magic-T is necessarily a 4 port circuit and always provides isolation between outputs. Baluns are critical building blocks for mixers and balanced amplifiers. Currently, Marki Microwave offers a class of ultra-broadband Baluns that operate from 200 khz to beyond 6 GHz. These broadband Baluns are ideal for use with high speed Analog to Digital converters. C. Amplitude Balance Amplitude balance is a measure of how evenly the power is split between the two arms of the device, and it is not applicable to directional couplers because they have an uneven power ratio. The amplitude balance is typically less than 0.25 db for Marki power dividers and 0.4 db for quad hybrid couplers. D. Amplitude Ripple Amplitude flatness is determined by how well the divider maintains the designing and specifying performance in datasheets. amplitude ratio over a specified bandwidth. Ideally the device would provide a perfectly flat (i.e. 0 db) ripple over the usable bandwidth. However, this is never the case and real devices will have some amount of amplitude ripple around the nominal splitting ratio. Typical values range from a few hundredths of a db to over 1 db depending on the design. In many designs, amplitude flatness can be traded for bandwidth. Hence, a 2-8 GHz device might specify a very flat 0.3 db ripple while a 2-18 GHz device might specify a 0.7 db ripple. Acceptable levels of amplitude ripple are application specific. Power dividers have better amplitude flatness than couplers, as a general rule. E. Phase Balance

14 Phase balance is a measure of the differential phase shift between the two output arms. Like Amplitude Balance, Phase Balance primarily applies to equal output power components like Wilkinson power dividers and quadrature hybrids. Most components provide a phase balance of a few degrees, and this balance tends to get worse at higher frequencies. F. Phase Ripple Like amplitude flatness, phase flatness corresponds to how well the constant relative phase shift is maintained throughout the bandwidth of the device. Well designed and packaged power dividers and couplers will fluctuate by only a few degrees over the entire usable bandwidth. Usually, the higher the operating frequency, the more difficult it is to maintain constant phase flatness. Phase error is mostly caused by small transmission line length asymmetries between the two output ports. This problem is exacerbated when there is poor VSWR matching at the ports. Careful design and packaging techniques help to maintain accurate phase flatness. E. Insertion Loss For power dividers and couplers, insertion loss refers to the additional loss above the nominal loss due to splitting. For example, in a 3 db power divider the insertion loss might be specified as 0.5 db. This implies that for a 0 dbm input signal, the two output signals will be approximately dbm each. The additional losses are caused primarily by reflections, dielectric absorption, radiation effects, and conductor losses. Broadband designs tend to have higher insertion losses because they are physically longer devices, and thus accumulate more dielectric, radiation, and conductor losses. Conductor losses in high frequency devices are caused predominantly by the skin effect and the surface roughness of PCB traces. Losses caused by reflections also increase with increasing frequency. G. Power Divider Isolation

15 In an ideal power divider the output ports are mutually isolated. In other words, a signal entering output 2 does not leak out of output 3. Isolation is defined as the ratio of a signal entering output #1 that is measured at output #2, assuming all ports are impedance matched (usually 50 ). Isolation values above 15 db are considered good, and some designs are better than others in terms of achievable isolation. A common engineering trade-off tends to exist in power dividers and couplers: the larger the bandwidth and the higher the frequency, the more difficult it is to provide good isolation. Resistive power dividers, for example, can achieve outstanding DC to 40 GHz coverage, but only provide 6 db of isolation. A Wilkinson power divider, on the other hand, can achieve isolations better than 20 db, but is impractical to build with bandwidths ratios greater than about 65:1. H. Coupler Isolation and Directivity Coupler isolation is different from power divider isolation because the coupler is a four port device. Coupler isolation measures the ratio between input power and power leakage from the isolated port. Typical values are db depending on the bandwidth of the device and the coupling ratio. To fairly measure the isolation of directional couplers with varying coupling ratios, another figure of merit called directivity is used. This is the ratio of coupled output power to leaked power from the isolated port, and can be calculated as the isolation in db minus the sum of the coupling ratio and insertion loss: Directivity (db) = ISO (CPL + IL) (1) In the above equation, all units are in db. As an example, a 20 db coupler might have an isolation of 40 db and an insertion loss of 0.04 db. Therefore, the directivity is calculated to be db. Directivity is an important figure of merit because it measures the ability of a directional coupler to distinguish between signals traveling in opposite directions. The higher the directivity, the better the coupler can distinguish between forward traveling and backward traveling waves. Referring to Fig., this implies that in an ideal

16 coupler port 3 will only see signals entering port 1 (the forward going wave), and will never see signals that enter from port 2 (the backward going wave). Any signal that enters port 2 and exits port 3 is considered a degradation in the directivity of the coupler. In test setups where we are interested in measuring reflections from a device under test, the directivity of the coupler establishes the uncertainty of the measurement. As with isolation, directivity is bandwidth dependent; narrow band couplers tend to have better directivity than broad band couplers. At Microwave, we optimize coupler directivity using modern numerical techniques to ensure state-of-the-art performance from a few hundred MHz to over 50 GHz. Our optimization techniques improve directivity by more than 10 db for most designs. I. VSWR/Return Loss The metrics voltage standing wave ratio (VSWR) and return loss answer the same question: how well is the RF network matched to a given load and source impedance? Unless otherwise stated, all Microwave components are designed to operate in 50 systems. For power dividers and couplers, one must work very hard to maintain a good 50 match over all frequencies to achieve the best performance, and to minimize reflections within the system. In fact, attributes like isolation and directivity are intimately related to the non-ideal 50 nature of the power divider or coupler. When building very high directivity directional couplers, for example, we work diligently to guarantee that the transmission lines are precisely maintained to 50, and that any errors caused by line discontinuities are minimized. In general, one cannot have good isolation/directivity without also having excellent return loss performance.

17 Table: Comparison of Various power dividers & couplers Resistive Power Divider Wilkinson Power Divider Directional Coupler Physics of Operation Resistive voltage divider circuit Quarter-wave transformer separates even and odd mode signals with an isolation resistor Weakly coupled quarter-wave transmission line sections Low Frequency Range DC 100s of MHz 100s of MHz High Frequency Range 10s of GHz 10s of GHz 10s of GHz Coupling Ratio 6 db 3 db 6 db 30 db Isolation 6 db 20 db 30 db 40 db

18 Lecturer-20 Microwave components & circuits find their use in a wide range including: 1) Wireless Communications (cellular, PCS) 2) Wireless Networking of applications, 3) Digital Communications (Ground-Ground, Satellite- Ground, Satellite-Satellite) 4) Radar Systems (ground based, airborne, personal vehicles) Target detection and identification, imaging (e.g., SAR) 5) Deep Space Communications Medical Imaging and treatment 7) Radio Spectrometry Microwave Circuit Design- Microwave Circuits are composed of distributed elements with dimensions such that the voltage and phase over the length of the device can vary significantly. By modifying the lengths and dimensions of the device, the line voltage (and current) amplitude and phase can be effectively controlled in a manner to obtain a specifically desired frequency response of the device. Microwave Circuits are used to design microwave amplifiers, oscillators, filters, power dividers/combiners, multiplexers, antennas and mixers. The necessary tools for the analysis and design of microwave circuit devices require an understanding of: transmission lines, two-port networks (Z, Y, ABCD Parameters), network theory (S-parameters), impedance matching, and filter design. What is the Microwave Circuit Designer s Duty for Wireless Systems? Designing filters, mixers, amplifiers, oscillators, matching networks, packaging, and system level design of the Analog and Digital Systems Designing the antennas and matching networks Propagation Affects (multipath, signal diversity) What are the principal future challenges? Miniaturized and low cost microwave circuitry (applies tocellular, PCS, GPS, on-board radar).

19 Direct hand held unit communication with low earth orbit and mid earth orbit satellites Direct high-speed digital communication with low earth orbit and mid earth orbit with portable computers. Miniature high-power amplifiers with low signal to noise ratios, miniature high-q filters, novel printed antennas, new packaging technology for combining RF and digital circuitry, reducing parasitics, improved modeling and analysis capabilities Cavity resonator- Cavity resonators are created by using bulk micro-machining, plating, and epoxy bonding the wafers together to generate buried cavities. The cavity can be either a typical waveguide structure (with and without obstructions) or a cavity containing transmission line resonating structures. The structure Can be made by bonding three wafers together with epoxy. The central wafer has the desired circuitry while the other two wafers form a shield cavity around the circuitry. Micro-machined low-loss transmission lines with gold metallization are used to define the circuitry in the cavity. Silicon is completely etched away from under the circuitry, until the circuitry is left on a thin dielectric membrane. At the same time, via grooves are opened all around the circuitry to ensure complete shielding. At the lower mode of frequencies the oscillation and amplification is carried out by conventional wires and transistors networks. We can design the oscillator with the use of coil and capacitors. We can also make an amplifier using transistors and FET s. At the higher mode of frequencies above 3 MHz all the methods mentioned above are not applicable due to the skin effect and stray inductance/capacitance. The cavity resonator is the device which is used for oscillation and amplification above 3 MHz efficiently.

20 It is a close compartment made of conductor and hollow from its interior. The input and output ports are made in this compartment to carry the R.F signal. The conducting area of the cavity works as inductors in parallel and its mouth works as the capacitors for the microwave length of frequencies. Hence, a perfect oscillator is formed when the input is provided to the cavity resonator at high frequency the output of the cavity resonator is higher than it input, so it also works as an amplifier. Types of Cavity Resonators The cavity resonator is designed in different types according to its structure and working capabilities. Some of the types are mentioned below. 1. Regulated Cavity Resonator 2. Un Regulated Cavity Resonator 3. Co-axial Cavity Resonator 4. Capacitive Cavity Resonator 5. Inductive Cavity Resonator 6. Waveguide Cavity Resonator 7. Reentrant Cavity Resonator 1. Regulated Cavity Resonator As shown in the given diagram. The regulated cavity resonator is designed in such a way that we take a piece of circular waveguide. This piece of circular waveguide is covered with the conducting plates from open ends. The input and

21 output ports are made in this piece in order to provide the external input to the cavity and obtain the output for further use. When the input is provided to the cavity, the oscillation takes place in the cavity at higher mode of frequencies. The E-field and the H-field is developed and the output is taken from the output port for further use. 1. Un-Regulated Cavity Resonator As shown in the given diagram, the un-regulated cavity resonator is designed in such a way that two pieces of regulated cavity resonator is joint together with the help of circular waveguide. In one piece of the regulated cavity resonator input port is made and in the second piece output port is designed. When the input is provided to the un-regulated cavity resonator the oscillation take place in this portion of the resonator. After a movement this oscillation is transferred to the output port gradually through the circular waveguide in the second piece of regulated cavity resonator. The advantage of un-regulated cavity resonator is its greater band width as compare to regulated cavity resonator. But the disadvantage is its less gain. 2. Co-axial Cavity Resonator

22 As shown in the given diagram, the co-axial cavity resonator is designed in the rectangular shape. In which internal portion is hollow. The surrounding is covered with the conduction mesh which is of the co-axial cable and the broad dimension is taken λ/2 of the operating frequency. The input and output ports are designed in the broad dimension of the resonator. The band width for this type of cavity resonator is high so that the wide range of input frequencies can be amplified. The waveguide is designed such a way that a piece of rectangular waveguide is taken and its open ends are covered by the conducting plates the input and output ports are made for the R.F energy in microwave length. When the input is provided to the waveguide cavity resonator the oscillation takes place. This oscillation is in such a way that E.Field is perpendicular to the broad dimension and H-field is perpendicular to the narrow dimension. The frequency of operation is equal to half wave length of the broad dimension.

23 Dielectric resonator- Lecturer-21 Obtaining transmission lines with low loss has always been a very challenging goal. Micromachining has enabled the fabrication of transmission lines on less than 2-µm thick dielectric layers. These transmission lines and resulting circuits have demonstrated zero dispersion, very low loss, and very small parasitics. The circuitry is patterned on a gold film located on a stress-compensated 1.4-:m membrane layer consisting of SiO2-Si3N4-SiO2 layer on a high resistivity silicon substrate using thermal oxidation and low-pressure chemical vapor deposition. The silicon is completely etched away from under the circuitry until the circuitry is left on a thin dielectric membrane. When applicable, the mating wafers are patterned, etched, plated, and mounted to the main wafer. Besides low loss transmission lines, inductors, resonators, and filters have been demonstrated based on this technology. Dielectric Resonator Oscillators (DRO) are used widely in today's electronic warfare, missile, radar and communication systems. They find use both in military and commercial applications. The DROs are characterized by low phase noise, compact size, frequency stability with temperature, ease of integration with other hybrid MIC circuitries, simple construction and the ability to withstand harsh environments. These characteristics make DROs a natural choice both for fundamental oscillators and as the sources for oscillators that are phase-locked to reference frequencies, such as crystal oscillators. This paper summarizes design techniques for DROs and the voltage- tuning DRO (VT-DRO), and presents measured data for them including phase noise, frequency stability and pulsing characteristics. Design Techniques

24 The design technique we will discuss is for a dielectric resonator (DR) to be used as a series feedback element. Practically, a GaAs FET or a Si-bipolar transistor is chosen as the active device for the oscillator portion of the DRO circuit. The Sibipolar transistor is generally selected for lower phase noise characteristics, while the GaAs FET is required for higher frequencies. For example, a DRO with a DR as a series feedback element can be designed using following design procedure: 1. Select an active device that is capable of oscillation at the design frequency, and use the small signal S-parameter of the device for the design. 2. Add a feedback circuit to ensure that the stability factor of the active device with the feedback circuit is less than unity with enough margin. 3. Create an active one-port analysis that consists of the active device, the feedback circuit, the matching network and the load as shown as figure1. Optimize Za (?) with the parameters in the feedback circuit and in the matching network to ensure that Ra (?0) is less than or equal to -25 ohms and Xa (?) has the possible maximum variation near resonance in order to insure high circuit Q. Determine the electrical spacing of the dielectric resonator such that the reactance it presents to the base or gate of the transistor is the negative of Za. The characteristic impedance of the output transmission line, Zg, is usually selected to be 50 ohms. The open stub (characteristic impedance of 50 ohms), which is terminated at the source end of the FET, serves as the feedback element. By adjusting the electric length of the feedback stub, various port impedance characteristics for Za (?) in the band of interest (6-15 GHz) can be obtained. From the port reactance characteristic, we observe that the shorter the electric length of feedback stub, the more rapid the port reactance change with frequency. On the other hand, for the active port, a shorter feedback stub induces higher negative resistance.

25 Finally, negative resistance is reduced if the electrical length of the feedback stub is less than 25 degrees. Taking etch tolerances into consideration, the length of the feedback stub is chosen as 45 degrees. Resonators (Filters) Resonators are a basic building block in frequency selective systems. Due to the diverse technologies involved and the low insertion loss associated with MEMS technology, several different resonator types exist. Three types of resonant structures, demonstrated over widely different frequency ranges, will be discussed: mechanical (300 KHz to 100 MHz), cavity (greater than 20 GHz), and piezoelectric film (1.5 to 7.5 GHz) resonators. Lecturer-22 Microstrip and Stripline Design INTRODUCTION Much has been written about terminating PCB traces in their characteristic impedance, to avoid signal reflections. However, it may not be clear when transmission line techniques are appropriate. A good guideline to determine when the transmission line approach is necessary for logic signals is as follows:

26 Terminate the transmission line in its characteristic impedance when the one-way propagation delay of the PCB track is equal to or greater than one-half the applied signal rise/fall time (whichever edge is faster). For example, a 2 inch microstrip line over an Er = 4.0 dielectric would have a delay of about 270 ps. Using the above rule strictly, termination would be appropriate whenever the signal rise time is less than approximately 500 ps. A more conservative rule is to use a 2 inch (PCB track length)/nanosecond (rise/fall time) rule. If the signal trace exceeds this trace-length/speed criterion, then termination should be used. For example, PCB tracks for high-speed logic with rise/fall time of 5 ns should be terminated in their characteristic impedance if the track length is equal to or greater than 10 inches (where measured length includes meanders). In the analog domain, it is important to note that this same 2 inch/nanosecond guideline should also be used with op amps and other circuits, to determine the need for transmission line techniques. For instance, if an amplifier must output a maximum frequency of fmax, then the equivalent risetime tr is related to this fmax. This limiting risetime, tr, can be calculated as: tr = 0.35/fmax Eq. 1 The maximum PCB track length is then calculated by multiplying tr by 2 inch/nanosecond. For example, a maximum frequency of 100 MHz corresponds to a risetime of 3.5 ns, so a 7-inch or more track carrying this signal should be treated as a transmission line. DESIGNING CONTROLLED IMPEDANCES TRACES ON PCBS A variety of trace geometries are possible with controlled impedance designs, and they may be either integral to or allied to the PCB pattern. In the discussions below, the basic patterns follow those of the IPC, as described in standard 2141A (see Reference 1). Note that the figures below use the term "ground plane". It should be understood that this plane is in fact a large area, low impedance reference plane. In practice it may

27 actually be either a ground plane or a power plane, both of which are assumed to be at zero ac potential. The first of these is the simple wire-over-a-plane form of transmission line, also called a wire microstrip. A cross-sectional view is shown in Figure 1. This type of transmission line might be a signal wire used within a breadboard, for example. It is composed simply of a discrete insulated wire spaced a fixed distance over a ground plane. The dielectric would be either the insulation wall of the wire, or a combination of this insulation and air. The impedance of this line in ohms can be estimated where D is the conductor diameter, H the wire spacing above the plane, and εr the dielectric constant. For patterns integral to the PCB, there are a variety of geometric models from which to choose, single-ended and differential. These are covered in some detail within IPC standard 2141A (see Reference 1), but information on two popular examples is shown here. Before beginning any PCB-based transmission line design, it should be understood that there are abundant equations, all claiming to cover such designs. In this context, "Which of these are accurate?" is an extremely pertinent question. The unfortunate answer is, none are perfectly so! All of the existing equations are approximations, and thus accurate to varying degrees, depending upon specifics. The best known and most widely quoted equations are those of Reference 1, but even these come with application caveats. MICROSTRIP PCB TRANSMISSION LINES For a simple two-sided PCB design where one side is a ground plane, a signal trace on the other side can be designed for controlled impedance. This geometry is known as a surface microstrip, or more simply, microstrip. For a given PCB laminate and copper weight, note that all parameters will be predetermined except for W, the width of the signal trace. These can then be used to design a PCB trace to match the impedance required by the circuit. For the signal trace of width W and thickness T, separated by distance H from a

28 ground (or power) plane by a PCB dielectric with dielectric constant εr, the characteristic impedance. Note that in these expressions, measurements are in common dimensions (mils). These transmission lines will have not only a characteristic impedance, but also capacitance. This can be calculated in terms of pf/in As an example including these calculations, a 2-layer board might use 20-mil wide (W), 1 ounce (T=1.4) copper traces separated by 10-mil (H) FR-4 (εr = 4.0) dielectric material. The resulting impedance for this microstrip would be about 50 Ω. For other standard impedances, for example the 75-Ω video standard, adjust "W" to about 8.3 mils. SOME MICROSTRIP GUIDELINES This example touches an interesting and quite handy point. Reference 2 discusses a useful guideline pertaining to microstrip PCB impedance. For a case of dielectric constant of 4.0 (FR-4), it turns out that when W/H is 2/1, the resulting impedance will be close to 50 Ω (as in the first example, with W = 20 mils). Careful readers will note that Eq. 3 predicts Zo to be about 46 Ω, generally consistent with accuracy quoted in Reference 2 (>5%). The IPC microstrip equation is most accurate between 50 and 100 Ω, but is substantially less so for lower (or higher) impedances. The propagation delay of the microstrip line can also be calculated, as per Eq. 5. This is the one-way transit time for a microstrip signal trace. Interestingly, for a given geometry model, the delay constant in ns/ft is a function only of the dielectric constant, and not the trace dimensions. Note that this is quite a convenient situation. It means that, with a given PCB laminate (and given εr), the propagation delay constant is fixed for various impedance lines. This delay constant can also be expressed in terms of ps/in, a form which will be more practical for smaller PCBs. Thus for an example PCB dielectric constant of 4.0, it can be noted that a microstrip's delay constant is about 1.63 ns/ft, or 136 ps/in. These two additional rules-of-thumb can be useful in designing the timing of signals across PCB trace runs.

29 SYMMETRIC STRIPLINE PCB TRANSMISSION LINES A method of PCB design preferred from many viewpoints is a multi-layer PCB. This arrangement embeds the signal trace between a power and a ground plane. The low-impedance ac-ground planes and the embedded signal trace form a symmetric stripline transmission line. As can be noted from the figure, the return current path for a high frequency signal trace is located directly above and below the signal trace on the ground/power planes. The high frequency signal is thus contained entirely inside the PCB, minimizing emissions, and providing natural shielding against incoming spurious signals. The characteristic impedance of this arrangement is again dependent upon geometry and the εr of the PCB dielectric. An expression for ZO of the stripline transmission line is: Here, all dimensions are again in mils, and B is the spacing between the two planes. In this symmetric geometry, note that B is also equal to 2H + T. Reference 2 indicates that the accuracy of this Reference 1 equation is typically on the order of 6%. Another handy guideline for the symmetric stripline in an εr = 4.0 case is to make B a multiple of W, in the range of 2 to 2.2. This will result in an stripline impedance of about 50 Ω. Of course this rule is based on a further approximation, by neglecting T. Nevertheless, it is still useful for ballpark estimates. The symmetric stripline also has a characteristic capacitance, which can be calculated in terms of pf/in For a PCB dielectric constant of 4.0, it can be noted that the symmetric stripline's delay constant is almost exactly 2 ns/ft, or 170 ps/in. SOME PROS AND CONS OF EMBEDDING TRACES The above discussions allow the design of PCB traces of defined impedance, either on a surface layer or embedded between layers. There of course are many other considerations beyond these impedance issues. Embedded signals do have one major and obvious disadvantage the debugging of the hidden circuit traces is difficult to impossible. Some of the pros and cons of embedded signal traces are summarized.

30 Multi-layer PCBs can be designed without the use of embedded traces, as is shown in the left-most cross-sectional example. This embedded case could be considered as a doubled two-layer PCB design (i.e., four copper layers overall). The routed traces at the top form a microstrip with the power plane, while the traces at the bottom form a microstrip with the ground plane. In this example, the signal traces of both outer layers are readily accessible for measurement and troubleshooting purposes. But, the arrangement does nothing to take advantage of the shielding properties of the planes. This non embedded arrangement will have greater emissions and susceptibility to external signals, vis-a-vis the embedded case at the right, which uses the embedding, and does take full advantage of the planes. As in many other engineering efforts, the decision of embedded vs. not-embedded for the PCB design becomes a tradeoff, in this case one of reduced emissions vs. ease of testing.

31 Lecturer-23 Microstrip or stripline? That choice has been faced by high frequency designers for decades. Both transmission-line technologies are widely used in both active and passive microwave circuits, with excellent results. Is one approach better than the other? Before tackling such a question, it might help to know how each transmission-line technology works and what kind of demands each place on a printed circuit board (PCB) material. Microstrip is a transmission-line format in which the conductor is fabricated on a dielectric substrate which itself has a bottom ground-plane layer. Conductors are usually formed by etching away unwanted metal from a conductor layer, such as copper. Stripline is often compared to a flattened coaxial cable in that, like the cable, it consists of an inner conductor completely surrounded by dielectric material which is itself surrounded by a ground braid or foil. Of course, stripline circuits are planar, so that they appear as a sandwich of conductors in the middle, surrounded by dielectric layers, which in turn have parallel ground planes on the top and bottom. Stripline circuits are usually fabricated by adhesively bonding a top-layer dielectric substrate/ground plane or prepreg with a single metal layer to a PCB laminate material on which circuitry has been photo-etched. To avoid unwanted propagation modes in stripline, the two ground planes must be shorted, often by means of shorting screws, or in the case of PCB technology, plated through hole via s. Why choose one transmission-line format over the other? Both provide excellent electrical performance through millimeter-wave frequencies, depending upon the choice of PCB materials. Microstrip circuits are easier (and less expensive) to fabricate than stripline, with less processing steps and easier placement of circuit components. The stripline format affords more isolation between adjacent circuit traces, supporting more densely integrated circuits than with microstrip. Stripline circuits are also well suited for fabricating multilayer circuits, with good isolation