This simple approach based on the use of wire lengths and chip resistors can be applied to equalize amplifiers for flat gain at millimeter-wave bandwidths.

Gain rolloff in broadband high-frequency amplifiers can be overcome by a number of strategies, including an easy-to-implement topology with two amplifiers and a microstrip filter. The simple use of bond wires and a pair of thin-film chip resistors can provide the response needed to flatten gain at millimeter-wave frequencies. These proven techniques have been used for amplifiers in radiometers of the PLANCK mission operating with 20-percent bandwidth at 30 GHz. The topology and approach can also be adapted to other frequencies.

Millimeter-wave monolithic-microwave integrated circuits (MMICs) are under development for a wide range of applications, including in automotive sensors, radiometers, communication system front ends, and radar systems.^{1} But the level of integration is still too low to avoid a large number of interconnects between MMICs.^{2}

Because MMICs are usually developed for microstrip environments, electromagnetic (EM) simulation tools are needed to model the waveguide-to-microstrip transitions required at millimeter-wave frequencies.

MMICs must be mounted inside cavities or channels acting as cutoff waveguides at the frequencies of interest to avoid unexpected couplings and resonances (waveguide moding). Careful simulation is important for minimizing loss with associated components and structures, including bends, tees, steps, and crossings. Wire bonding or ribbon lengths and grounding are also critical. Modeling must also consider such factors as thermal expansion between components and substrates.^{3}

Gain-slope equalization at RF and microwave frequencies has been traditionally handles by the use of a modified tee attenuator with parallel capacitor and series inductor.^{4}

At millimeter-wave frequencies, not only lumped elements but distributed circuit elements must be used for equalization.^{5-7} Design procedures have been developed for equalizing filters at RF and microwave frequencies.^{8} But translation of a lumped-element RF equalizer to millimeter-wave frequencies is not trivial. Fortunately, a simple topology has been developed to provide equalization at millimeter-wave frequencies. Used for the 30-GHz back-end module of the Planck mission's radiometer, the hybrid approach works with two MMIC amplifiers and a bandpass filter to provide flat, broadband gain at millimeter-wave frequencies.

The classic solution for RF equalization consists of a simple network to compensate for losses at higher frequencies, such as in a cable-television (CATV) distribution cable.^{4}

Figure 1 shows a network which provides matching and equalization at the same time, where impedances Z_{1} and Z_{2} should fulfill the condition:

Z_{1}Z_{2} = R_{0}^{2}

where:

R_{0} = the reference impedance.

Figure 2 shows an approach for implementing Z_{1} and Z_{2}. Resistors R_{1} and R_{2} set the DC attenuation and preserve matching:

where:

k = 10exp.

The resonance frequency of L_{2} and C_{1}2C_{1})_{0.5}> corresponds to a frequency where the gain is 3 dB below the maximum gain. Figure 3 shows |S_{21}| for three ideal equalizers designed for the band between 40 and 600 MHz, with the slope fixed to provide 6.5-, 10.5-, and 21-dB attenuation at DC.

At higher frequencies, ref. 5 proposes simple gain compensating networks (Fig. 4). At the maximum gain frequency, series resonance (L_{s} − C_{s}) shows a short circuit and parallel resonance (C_{p} − L_{p} , in series with a resistor) shows an open. Resonant impedances can be implemented with lumped or distributed elements. For example, a parallel resonator can be implemented with a quarter-wavelength short-circuited stub.

Reference 5 provides closed design formulas to choose the values of all the parameters according to the required slope. Reference 6 offers a similar topology, with resistive loaded shunt stubs and series resonators.

The main goal of the Planck Mission is to measure anisotropies in the cosmic microwave background (CMB). Measurements are made by satellite-based cooled front-end modules (FEMs) followed by back-end modules (BEMs). Each BEM consists of several amplification-filter chains and associated detectors, which provide a DC level proportional to the power level received from the CMB. Of particular interest is the 30-GHz BEM which has a 20-percent fractional bandwidth, where the amplifiers must provide flat gain in a band from 27 to 33 GHz. Gain ripple should be as small as possible to avoid reducing the effective bandwidth of the radiometer. Available MMIC amplifiers can't provide such flat gain, so additional components were required.

Two MMIC amplifiers from Hittite Microwave (model HMC 263) were cascaded. Single on-wafer measured S-parameters were used for an estimation of the whole transfer function shape and the gain rolloff, adding the effect of interconnection microstrip lines and the waveguide-to-microstrip transition. A gain slope of around 6 dB was found between 27 and 33 GHz (1 dB/GHz). Figure 5 shows the |S_{21}| performance for the amplification chain without compensation.

To implement equalizers at millimeter-wave frequencies, several restrictions were in order:

- The space for an equalization network was limited to a 2.6-mm channel width (to ensure nonpropagating modes other than microstrip:waveguide modes),
- Components are limited at these frequencies, and
- Component tolerances and manufacturing variations will limit performance.

The synthesis formulas used at lower frequencies lead to impractical line lengths or too-small values of series capacitors, requiring different topologies. The proposed topology (Fig. 6) consists of a microstrip line section with a wire bonded to one pad of a chip resistor, the other pad left open, and the backside grounded, placed close to the microstrip line.

The wire over substrate has been modeled as a transmission line due to the length of the wire.^{10} The wire ends on a resistor with the other terminal left open (open effect included). Parasitic capacitances are used as part of the LC series resonator, together with the wire.

Quarter-wavelength wires are used as RF chokes for microstrip high-frequency circuits because they can show an open-circuit impedance at their input if they are terminated with a short (capacitor) at the other side. This approach is proposed for use here, bu shifting the quarter-wavelength frequency beyond the upper band of interest to achieve the desired trap effect in the lower part of the band.

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The proposed structure includes not only a wire plus a capacitor (short approach) but also a chip resistor. The resistor adds power-dissipating capability; its parasitic elements provide the required capacitance. The length of the wire is a critical parameter for tuning minimum attenuation. The parasitic capacitance of the resistor resonates with the wire (as an inductor) at a frequency above the maximum frequency of the desired passband. The value of the resistor determines the attenuation slope, mismatching, and insertion losses.

MATLAB computer simulations were performed to validate the proposed structure, by modeling a parallel admittance consisting of a wire over alumina substrate as a transmission line (with characteristic impedance and velocity of propagation per ref. 10). The line was terminated with a 1-kΩ chip resistor (including parasitic capacitances). Figures 7 and 8 show results for a 25-µm-diameter wire, varying wire length from 0.5 to 1.1 mm and sweeping the test frequency from 20 to 40 GHz.

Equalization is achieved by a combination of dissipation and mismatching. Once the equalization effect was initially modeled, a more practical simulation was carried out on a circuit simulator including input and output microstrip lines on two substrates 2O_{3} (alumina) and MetClad^{®} (with dielectric constant of 2.17)> and the complete 1-kΩ chip-resistor model. The wire diameter was fixed to 25 µm and the wire length was swept. The simulated |S_{21}| results for wires with different lengths on the two substrates are shown in Figs. 9a and 9b. The values are not enough to achieve the desired 6-dB slope with minimum losses at the top of the band. A lower-valued resistor can increase the slope, but with an increase in minimum attenuation. The solution proposed consists of adding two traps but trying to avoid mutual interference by means of quarter-wavelength spacing between them.

To increase equalization and preserve minimum attenuation at the higher part of the band of interest, two traps were cascaded, but separated by one-quarter wavelength to avoid mutual interaction (Fig. 10). The number of wire resistors placed along the microstrip line, and spaced by one-quarter wavelength, can be increased if a sharper slope is required. In this analysis, both substrates (Al_{2}O_{3} and MetClad) were considered, changing the optimum distance between wires due to changes in wavelength.

Simulated results of the double trap alone for several wire lengths are shown in Fig. 11a for the Al_{2}O_{3} substrate and in Fig. 11b for the MetClad substrate. The compensated gain slope is around the goal of 6 dB, without increasing the minimum attenuation. Figure 12 shows the results of studying the effects of distance between wires. The simulation of S_{21} for fixed wire length and different distances between wires shows great tolerance to variations.

Compensation values from 6 to 9 dB can be achieved with two traps in the band of interest (from 27 to 33 GHz). Wire diameter is also a critical parameter, but it is usually fixed from the beginning to some of the standard values (17.5 µm and 25 µm). Using the thickest wire, the longest length is needed for the same equalization profile. If the length of the wire becomes too short for practical purposes, a thicker wire should be used, or two wires used together to make the length less critical.

An Al_{2}O_{3} microstrip circuit was built to check the compensating effect in the frequency response. Figure 13 shows a photograph of the circuit and |S_{21}| measurements are plotted in Fig. 14. Coplanar-to-microstrip transitions for on-wafer measurements were used to place the reference plane for measurements right on the alumina edges, avoiding difficult-to-de-embed coaxial connector parasitic elements.^{11}

The results were compared to simulations for different wire lengths in the range of tolerances, using an improved model of the chip resistors parasitics based on the authors' resistor impedance measurements. Reasonable agreement was achieved (Fig. 15).

Following the successful results of the isolated alumina double-trap measurements, the equalizer was incorporated into the amplification chain. It followed two MMICs and before a microstrip coupled-line bandpass filter. The filter was developed according to procedures described in ref. 3. Figure 16 shows global gain results for three different wire lengths on alumina (compare with Fig. 5). The table (Figs. 17 and 18) provides recommended parameters for fabricating a double trap on the two different substrate materials.

ACKNOWLEDGMENTS

This work has been supported by the Plan Nacional de I+D+I, Programa Nacional de Espacio, ESP2002-04141-C03-01/02/03. The authors would like to thank Eva Mª Cuerno and Elena Alexandrina Pana for their assistance in the assembly of these circuits.

REFERENCES

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