Broadband Microwave Distributed Amplifier

Broadband Microwave Distributed Amplifier KEVIN BOWERS and PATRICK RIEHL Abstract—We present an analysis of distributed amplifiers II. DISCRETE TRANSMISSION LINES suitable for use in the microwave regime. From this we In order to derive design formulae for a FET DA, evaluate several designs using ideal components and the UC- Berkeley 217 GaAs FET. Alterations to the basic design we must first consider propagation of waves on discrete including the use of CASCODE and CASCODE gain cells and transmission structures. Alternative treatements can be 4 the use of series capacitors on the gate lines are discussed. We found (Pozar, op. cit. and in ). Consider the following implement a final design using microstrip components. The 5- circuit (Z and Y are arbitrary complex impedances and all stage design achieves 19.4 dB of power gain (+/- 1.2 dB) from voltages and currents are phasors): 0.1 to 14.3 GHz. Reflected power at the input and output from loads matched to 50 Ohms are all below –20 dB over the in-1 in in+1 in+2 bandwidth of the device, as is power transmitted from the Z/2 Z/2 Z/2 Z/2 Z/2 Z/2 output to the input. The device is stable for broad range of + + + + + Vn-1 Y Vn Vy Y iy Vn+1 Y Vn+2 input and output loads. A novel matching network has been - - - - - designed to minimize reflections along the gate and drain lines d over all frequencies and eliminate resonant peaks that are a potential cause of instability externally. Measurements suggest Applying Kirchoff’s laws to the circuit we arrive at the the design is internally stable as well. following equations: Index Terms—distributed amplifier, broadband amplifier, microwave circuits i = Yv y y i = i + + i i − (ZY + 2)i + i = 0 n n 1 y ⇒ n−1 n n+1 I. INTRODUCTION − = 1 − − 1 + = vn vy 2 Zin vn vn+1 2 Z(in in+1) 0 he principal of distributed amplification was originally 1 v − v = 1 Zi Tapplied to vacuum tubes structures . The principle has y n+1 2 n+1 been applied in many other devices, including lasers, traveling wave tubes and, most relevant to us, microwave Assuming traveling waves on the circuit of the form, amplifiers. Because of its broad range of applications, − θ − θ = j n = j n , we obtain the following extensive literature exists on the subject. 2,3 contain many vn Ve ,in Ie references to this literature. expressions for the wave impedance and phase shift per In a common source microwave FET distributed segment: amplifier, a discrete component transmission line is constructed out of the gate - source input admittance - the θ = cos−1(1+ 1 ZY ) = 2sin −1 − 1 ZY gate line. Another (ideally) identical transmission structure 2 4 is drain - source input admittance – the drain line. If the = Z 1 θ = Z + 1 Zline Y cos 2 Y 1 4 ZY transmission structures are identical, a wave can be launched on the gate line and be coherently amplified onto For a line consisting of ideal shunt capacitors and ideal the drain line. It is a simple matter to construct transmission series inductors we have: lines with identical properties on the gate and drain lines assuming a unilateral transistor over a very wide range of frequencies. Thus these devices are naturally broadband. = L − ω 2 ω = 2 Zline C 1 ω 2 where c . Also, by using FET parasitics as a part of the transmission c LC lines, some FET limitations can be avoided. In this report, we evaluate several designs subject A parallel analysis for a π section discrete transmission line to the design goal of maximizing gain bandwidth product. yields: The designs attempt to match the impedance of the input and output ports to 50 Ohms over the bandwidth of the = L − ω 2 Zline C / 1 ω 2 device. We also try to achieve as much gain flatness as c possible. The designs only use the UC-Berkeley 217 GaAs FET and are easily implemented using microstrip components; undesirable components such as spiral inductors are avoided. From this we see that the impedance of the line is IV. DESIGN REVIEW AMPLIFIER frequency dependent and the line has a cutoff frequency This design approach discussed above can be such that no waves of higher frequency can propagate. improved by optimizing the lines for phase shift per In a typical FET implementation the shunt segment and impedance. The scattering parameters shown capacitors are partly provided by the FET and transmission in Figure B3 were presented in the 217 Design Review. The lines serve as the inductors. Thus, for a given impedance for component values used were: the line, the gate source (or drain source) capacitance becomes a limiting factor to the bandwidth for the L = 0.39751 nH amplifier. g Cga = 0.32036 pF Ld = 0.40772 nH III. “RULE OF THUMB” FET DISTRIBUTED AMPLIFIER Cda = 0.057345 pF FORMULAE Nsections = 10 Below a simple FET DA is shown: The optimization accounted for the drain source resistance Drain Line (Rds - in parallel with Cds) and gate source input resistance Cda Cda Cda (Ri - in series with Cgs). The following function was Ω ... 50 Pout minimized: Ld/2D Ld/2 Ld/2D Ld/2 Ld/2D Ld/2 S S S Cga Cga Cga ... Ω = Γ + Γ + θ − θ Pin 50 f (Lg , Ld ,Cga ,Cda ) ∑a g b d c Re g Re d Lg/2 Lg/2 Lg/2 Lg/2 Lg/2 Lg/2 design Gate Line freqencies In the ensuing analysis, we assume an idealized FET model: Γg and Γd are the reflection coefficients of the gate and drain lines off a 50 Ohm resistor respectively. Similarly, θ θ GDRe g and Re d are the phase shifts per section of waves + gmVgs traveling on the gate and drain lines. (a,b,c) are adjustable D Cgs Vgs Cds weights (chosen such that the terms of the initial guess S - contributed in the ratio 4:2:1). The initial guess was chosen S S by the Rule of Thumb rules with Cga = 3Cgs. The design frequencies were at 1,2,4,8 and 16 GHz. The Nedler-Mead simplex method was used (MATLAB function “fmins”) to In order to match the phase shifts on both the gate minimize the function. and drain lines while matching the impedances to 50 Ohms, The optimal number of sections to use was we must have: computed at 16 GHz from the following formula (given in Pozar, op.cit. ): Cgs // Cga = Cds + Cda ln(α l /α l ) and N = g g d d opt α l −α l 2 g g d d Ld = Lg = (50Ω) ( Cgs // Cga ) where the loss per section on the gate and drain lines is For this values, the impedance of the gate and drain lines is given by: well-matched to 50 Ohms for frequencies well below the cutoff of the line. We will do a better job of matching later. α = − θ α = − θ The above relations leave Cda unspecified. For a glg Im g , d ld Im d positive capacitance in a FET with Cgs > Cds, as is true for nearly all FETs, the two extremes are Cda = 0 (Cda is an The resulting amplifier achieved 20 dB of power open circuit) and Cda = Cgs – Cds (Cga is a short circuit). gain over a bandwidth of about 25 GHz. The scattering A four section distributed amplifier was designed parameters can be found in Figure B3. It should be noted with the above relations for the two extreme cases. Figure that gain is achieved in this amplifier beyond fT of the 217 B1 shows the result of equalizing the lines to Cds and Figure FET (21 GHz). Physically this is because the FET parasitics B2 shows the result of equalizing the lines to Cgs. The Cgs and Cds now work in favor of the design . greater bandwidth of figure B1 is apparent (about 50 GHz), however, the design does not achieve any amplification. V. GAIN BANDWIDTH TRADEOFF THE SERIES The design in Figure B2 has substantially less bandwidth CAPACITANCE ON THE GATE LINE (about 20 GHz), but it does achieve a power gain of about 16 dB. Since Cga improved the bandwidth at the expense of gain, it is desirable to know the optimal value of Cga for gain bandwidth product for a given number of sections. This may be crudely estimated by noting that the presence of Cga makes the voltage across Cgs equal to (in the case of filter section was designed such that its infinite attenuation an idealized FET): peak is placed at the frequency of the resonant peak. The m- derived filter section unfortunately cannot be exactly ω matched to the gate and drain lines because the cutoff 1/ j Cgs 1 Cgs V = V = V , x = frequency of the gate / drain line is above the resonant gs,n g,n ω + ω g,n + 1/ j Cgs 1/ j Cga 1 x Cga frequency we are trying to eliminate (for an m-derived filter section, the cutoff frequency is always below the infinite where Vg,n is the voltage on the n-th section of the gate line attenuation frequency). Thus for the final design, the input at the shunt element. The power gain of such an amplifier is and output an m-derived filter section is matched to 50 thus proportional to (1+x)-2. Ohms. This section is placed at the input and output of the gate and drain lines (which in turn are matched to 50 Ohms Likewise cutoff frequency of the gate line can be written with the m-derived bisected π sections discussed above).

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