射频混频器设计Harmonic balance simulation speeds RF mixer design-2
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.
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
(1)
where V0 is the excitation vector. The output current vector IL is
(2)
where SI is the modal current matrix, SV is the modal voltage matrix, 1 is the identity matrix, and L is the diagonal matrix,
(3)
where n are the propagation constants of each mode and L is the length of the coupled- line structure. 2L is a similar matrix having 2L instead of L. These expressions realize the first column of the admittance matrix,
(4)
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.
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
This mixer exhibits low conversion loss, high isolation, and excellent intermodulation performance from 26-40 GHz. The IF frequency range is DC- 12 GHz.
It consists of Marchand baluns for both the RF and LO, and a second "horseshoe" balun for IF extraction and further even-mode rejection.
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 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.
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
*A version of this paper was presented at the 1999 Wireless Symposium.
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.
