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 Z₁ and Z₂ should fulfill the condition:

Z₁Z₂ = R₀²

where:

R₀ = the reference impedance.

Figure 2 shows an approach for implementing Z₁ and Z₂. Resistors R₁ and R₂ set the DC attenuation and preserve matching:

where:

k = 10exp[AT(dB)/10].

The resonance frequency of L₂ and C₁ [1/2π(L₂C₁)_0.5] corresponds to a frequency where the gain is 3 dB below the maximum gain. Figure 3 shows |S₂₁| 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 |S₂₁| performance for the amplification chain without compensation.

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

1. The space for an equalization network was limited to a 2.6-mm channel width (to ensure nonpropagating modes other than microstrip:waveguide modes),
2. Components are limited at these frequencies, and
3. 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.