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”

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 µm) 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

LO

RF

IF

IF Blocking Capacitors

IF Return

Diode “Quad”

Figure 1. A common type of commercial, suspended-substrate diode mixer. The compos-ite, low-dielectric-constant substrate is very thin (typically 125-250 µm) and is mounted in a housing or carrier. An open area under the substrate is essential.

Output

Input λ/2

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 imped-ance is made as great as possible.

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

(1)I0 SI 1 Γ2L+( ) 1 Γ2L–( ) 1– SV1– V0=

Figure 3. Performance of a somewhat idealized Marchand balun with Z0o = 25Ω, Z0e = 180Ω, and ZL = 60Ω. 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.

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 ΓL is the diagonal matrix,

(3)

where γn are the propagation constants of each mode and L is the length of the coupled-

line structure. Γ2L 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.

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

IL 2SIΓL 1 Γ2L–( ) 1– SV1– V0–=

ΓL

jγ1L( )exp 0 0 0

0 jγ2L( )exp 0 0

0 0 … 0

0 0 0 jγnL( )exp

=

I0

IL

Y0 0, Y0 L,

YL 0, YL L,

V0

VL

=

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

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[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.