martes, 2 de febrero de 2010

Computer-Aided Design of RF and Microwave Mixers

 S. A. Maas Applied Wave Research, Inc. 1960 E. Grand Ave., Suite 530 El Segundo, California, 90245 USA smaas@mwoffice.com



Abstract

This paper describes the current state of the art in the design, analysis, and computer modeling of microwave and RF mixers. We show how modern computer analysis (CAD) tools, especially general-purpose harmonic-balance simulators and planar electromagnetic simulators, have improved both the quality of mixer designs and the efficiency of the design process. Simultaneously, new approaches to the design of baluns and passive structures have resulted in high-performance, broadband designs. As a result, mixer technology has reached a high level of maturity.
Introduction
Since the invention of the superheterodyne receiver by Edwin Armstrong in 1917, mixers have been essential parts of radio communication systems. Mixer design has traditionally been an approximate process, at best using special-purpose computer programs. The development of general-purpose harmonic-balance simulators and electromagnetic simulators, however, has improved the accuracy of the design process enormously, and it has even made the design of a wide variety of new balun structures possible. These have been particularly valuable in monolithic circuits.
Mixers can be broadly categorized as active or passive. Passive mixers primarily use Schottky-barrier diodes, although a relatively new type of passive mixer, the FET resistive mixer [1], recently has become popular. FET resistive mixers use the resistive channel of a MESFET to provide low-distortion mixing, with approximately the same conversion loss as a diode mixer. Active mixers use either FET or bipolar devices. FETs (either MESFETs or HEMTs) are used for most microwave and RF applications where active mixers are employed; BJTs and occasionally HBTs are used most frequently as Gilbert multipliers [2] for modulation, phase detection, and similar purposes. The theory of both active and passive mixers has been well known for some time [3 - 8].
Mixer Types and Technologies
Although single-device mixers occasionally are used, most practical mixers are balanced. Balanced mixers require baluns or hybrids, and these largely determine the bandwidth and
 
overall performance of the mixer. Thus, they are the subject of considerable research interest. In this paper, we shall consider only balanced mixers.
In spite of the maturity of FET circuits, diode mixers are still widely used in microwave circuits. Diode mixers have an important advantage over FETs and bipolar devices: a Schottky-barrier diode is inherently a resistive device, and as such has very wide bandwidth. The bandwidths of diode mixers are limited primarily by the bandwidths of the baluns, not the diodes. FETs, in contrast, have a high-Q gate-input impedance, causing difficulties in achieving flat, wide bandwidth.
Diode mixers usually have 5-8 dB conversion loss, while active mixers usually can achieve at least a few dB of gain. Although properly designed active mixers can achieve somewhat lower noise figures than diode mixers, most systems can tolerate a relatively noisy mixer, so the diode mixer’s loss and noise are rarely a significant disadvantage. Broadband diode mixers usually do not require more local-oscillator (LO) power than active mixers, but narrowband active mixers may have an LO-power advantage. Finally, balanced active mixers always require an IF hybrid or balun; diode mixers generally do not. When the IF frequency is low, the resulting large size of the IF balun may be troublesome, especially in monolithic circuits. Finally, even balanced active mixers require matching and filtering circuits, while balanced diode mixers largely do not.
Active mixers have a few important advantages over diode mixers besides their superior gain and noise figure. High-quality diodes are often difficult to produce in FET monolithic circuit technologies, so active FET mixers often are easier to integrate. Diodes in such technologies usually consist of a FET gate-to-channel junction, which usually is a very poor diode. Dual-gate FET mixers offer inherent LO-RF isolation, even in single-device circuits, although noise figure and gain usually are slightly worse than in single-gate FET mixers.
Mixer Design
The design of balanced mixers—passive or active—involves two fundamental tasks: (1) design of the baluns and passive matching circuits, and (2) design and analysis of the complete mixer. We consider these topics individually.
Balun and Passive-Circuit Design
The design of baluns for discrete-component mixers is very mature. Figure 1 shows a common structure. In this mixer, the baluns consist of simple, parallel-coupled strips mounted on a suspended substrate. Often, the lower strip (which is connected to the ground surface of the housing) is tapered to improve the balun’s performance.
Such baluns are clearly impractical in monolithic circuits, and attempts to “translate”
 
 

Figure 1. A common type of commercial, suspended-substrate diode mixer. The compos-ite, low-dielectric-constant substrate is very thin (typically 125-250 mm) and is mounted in a housing or carrier. An open area under the substrate is essential.
suspended-substrate baluns into planar monolithic form have been largely unsuccessful. The fundamental problem is in the extra capacitance between the monolithic circuit’s microstrips and ground. Because the substrate is thin (usually 100 mm) and has a high dielectric constant (12.9), this capacitance is unavoidably large. It allows an even mode to exist on the balun. The even mode unbalances the mixer and allows input-to-output coupling, which reduces port-to-port isolation. Unless special efforts are made to reduce it, the imbalance is severe.
Practical approaches to the design of broadband monolithic baluns are still scarce. We have centered on the Marchand balun as a building block for broadband, planar monolithic mixers. Although its even-mode characteristic impedance is no higher than that of other structures, its performance tolerates low even-mode impedance much better.



Figure 2 shows a planar Marchand balun, and Figure 3 shows its calculated performance. Clearly, the Marchand balun is intrinsically capable of good performance over a
 
 
Figure 2.   A planar Marchand balun consists of two quarter-wavelength coupled-line sec-tions. The odd-mode characteristic impedance is chosen so that the structure acts as a transformer between the source and load, and the even-mode impedance is made as great as possible.
 
 
Figure 3.  Performance of a somewhat idealized Marchand balun with Z0o = 25W,

Z0e = 180W, and ZL = 60W. The output terminals are each treated as separate ports. The even- and odd-mode phase velocities are equal, causing the balance to be (theoretically) perfect.
multioctave band. In less idealized cases, we find that an octave bandwidth, or slightly greater, is practically achievable.
We have experimented extensively with Marchand baluns and Marchand-like balun structures. Inevitably we find that a three-strip structure gives the best trade-off between odd-mode and even-mode impedances. Unfortunately, such asymmetrical coupled-line structures are not simple to analyze.
Our approach to analysis of these structures is as follows. We use a quasistatic, moment-method electromagnetic simulator called LINPAR [9] to determine the current and voltage modes on the coupled-line structure used in the balun. We then import these data into our circuit simulator, where length information is introduced and a Y matrix for the coupled-line structure is created. The circuit can then be analyzed directly in the linear-circuit simulator or as part of a complete mixer by harmonic-balance simulation. A coupled-line structure having arbitrary line widths and spacings can be analyzed in this manner.
The coupled-line structure’s admittance matrix can be determined from its length, its modal matrices, the modal phase velocities. The vector of input current I0 of a set of coupled lines with a short-circuited output is

where V0 is the excitation vector. The output current vector IL is
 

where SI is the modal current matrix, SV is the modal voltage matrix, 1 is the identity matrix, and GL is the diagonal matrix,
 

where gn are the propagation constants of each mode and L is the length of the coupled-line structure. G2L is a similar matrix having 2L instead of L. These expressions realize the first column of the admittance matrix,
 
The rest of the matrix can be filled in from the obvious symmetries.
This process has two important advantages compared to a general-purpose planar electromagnetic simulator using spectral-domain moment methods or other full-wave approaches. First, it is much faster, and more variations of the coupled-line geometry can be studied in limited time. Second, the length of the structure is not specified until the circuit analysis is performed, so the length can be optimized within the circuit simulator. This results in a very efficient design process.
A disadvantage of this method is the quasistatic nature of the electromagnetic analysis. This is less of a difficulty than one might initially imagine, since non-TEM dispersion effects are generally insignificant in monolithic baluns at frequencies below ~50 GHz, and probably, in many cases, higher.
Mixer Circuit Analysis
Harmonic-balance analysis is the method of choice for designing RF and microwave
mixers. Time-domain analysis (for example, SPICE [10]) may also be acceptable in some
cases.
In “classical” harmonic-balance analysis [5], only a single excitation tone is used. The method has been extended, however, to allow two or more noncommensurate excitation frequencies. These methods increase the number of frequency components in the analysis and slow the analysis significantly. Several methods can be used to improve the efficiency of mixer analysis by multitone harmonic balance. One is to select the frequencies in the
 
analysis so they include only the LO harmonics and sidebands around each harmonic. This reduces the size of the frequency set considerably, and thereby improves efficiency. Another is to use conversion-matrix analysis. In this method, the mixer is first analyzed under LO excitation alone, and then a noniterative calculation, treating the RF as a small deviation on the LO voltage, follows. This process is very efficient, because the computation time required for the conversion-matrix analysis is usually insignificant, and the harmonic-balance analysis is single-tone. Conversion-matrix analysis is applicable to both active and passive mixers.
Numerical optimization of mixer designs is possible in most harmonic-balance simulators, but the time required for such optimization is usually prohibitive. A more intelligent design process usually obviates such optimization, or at least reduces considerably the amount needed. We begin with an idealized circuit, using only lumped or simple distributed components, and baluns are replaced by transformers. We then determine input and optimum load impedances, and we design simple matching networks, usually lumped-element. The circuit is again optimized, the ideal elements are replaced one-by-one with real structures, and the mixer’s performance is recalculated, reoptimized, and maintained throughout the process. When the finished circuit emerges, it needs little or no numerical optimization.
Design Examples



Figure 4 shows a planar star mixer using three-strip Marchand baluns in a coplanar-waveguide (CPW) structure. We have designed a large number of mixers of this type, most
 
 

Figure 4.
 
A planar star mixer uses three-strip Marchand baluns in a CPW-like configura-tion. This mixer exhibits low conversion loss, high isolation, and excellent intermodulation performance from 26-40 GHz. The IF frequency range is DC-12 GHz.
 
operating over octave bandwidths between 12 and 45 GHz. The mixer shown in the figure operates over a 26-40 GHz RF and LO band and a DC-12 GHz IF band. Conversion loss is 7 to 9 dB over this frequency range. The RF-to-LO isolation, probably the best indication of the balun’s effectiveness, is greater than 40 dB. This is the first mixer of this type that we developed; subsequent mixers have exhibited 18 GHz IF bandwidth, 20 to 40 GHz RF and LO bandwidth, and lower conversion loss. These mixers typically exhibit input third-order intercept points above 20 dB.
Figure 5 shows a rather unusual mixer that makes extensive use of coupled-line baluns. The RF and LO baluns are multistrip, asymmetrical Marchands. One of the quarter-wave sections of each balun is the usual three-strip structure, while the other has six equal-width, equally spaced strips. The large number of strips gives the section a very low odd-mode impedance, which improves the bandwidth considerably.
The RF balun excites a curved, coupled-line section which we have come to call the horseshoe. This section has two purposes: first, it provides an approximate virtual-ground point for an IF connection, always a difficulty in microwave ring mixer designs. Second, it improves the balun’s balance. This mixer exhibits low conversion loss (~7 dB) and high RF-LO isolation (~35 dB) over an 18-40 GHz band. Unfortunately, the LO-to-IF and RF-to-IF isolations are only modest, approximately 13 dB. Subsequent designs used a stub in the IF connection to improve the rejection.
 
 


Figure 5.
 
This planar ring-diode mixer operates from 18 to 40 GHz, with a 12-GHz IF. It consists of Marchand baluns for both the RF and LO, and a second “horseshoe” balun for IF extraction and further even-mode rejection.
 
Conclusions
The use of modern harmonic-balance simulators and electromagnetic analysis software has been instrumental in the design of modern mixers. Especially, it has allowed the development of new types of balun structures, without which broadband monolithic balanced mixers would be impossible. Design techniques, however, must be adjusted to make most efficient use of these technologies. The result is high-performance, low-cost circuits operating into the millimeter-wave region.
References
[1]      S. Maas, “A GaAs MESFET Mixer with Very Low Intermodulation,” IEEE Trans. Microwave Theory Tech., vol. MTT-35, no. 4, p. 425, April, 1987.
[2]      B. Gilbert, “A Precise Four-Quadrant Multiplier with Subnanosecond Response,” IEEE J. Solid-State Circuits, vol. SC-3, p. 365, Dec., 1968.
[3]      A. A. M. Saleh, Theory of Resistive Mixers, MIT Press, Cambridge, MA 1971.
[4]      S. Egami, “Nonlinear, Linear Analysis and Computer-Aided Design of Resistive Mixers,” IEEE Trans. Microwave Theory Tech., vol. MTT-22, p. 270, 1974.
[5]      S. Maas, Nonlinear Microwave Circuits, Artech House, Norwood, MA, 1988.
[6]      S. Maas, Microwave Mixers, Second Edition, Artech House, Norwood, MA, 1992.
[7]      S. Maas, “Theory and Analysis of GaAs MESFET Mixers,” IEEE Trans. Microwave Theory Tech., vol. MTT-32, no. 10, p. 1402, Oct., 1984.
[8]      R. A. Pucel, D. Masse’, and R. Bera, “Performance of GaAs MESFET Mixers at X Band,” IEEE Trans. MTT, vol. MTT-24, no. 6, p. 351, June, 1976.
[9]      A. R. Djordjevic et al., LINPAR for Windows, ver. 2.0, Artech House, Norwood, MA 1999.
[10]    SPICE3, Electronics Research Laboratory, University of California, Berkeley, CA USA 94720.




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