A broadband low-noise amplifier can be designed based on Takahasi's results. This design method bypasses the gain bandwidth theory and generates lumped-element lossless networks, which are easily converted to distributed elements for matching. An Excel program has been designed to synthesize the input and output matching networks. The validity of the design is verified using Genesys V8. Optimization is further used that requires several quick iterations to achieve the performance.

The GaAs FET is first modeled using formulas derived by D. J. Mellor. The Excel program can model the input and output impedance of the device into series R_iL_iC_i and series L_o, shunt R_o-C_o circuit, respectively. The device is assumed unilateral for this purpose, which reduces the transistor modeling problem.

For the Chebyshev low-pass ladder networks, the transducer power gain response G (w²) is given by G (w²) = K_n / [1+e² C_n² (w)], 0 ≤ K_n ≤1 where K_n is the gain factor of G (w²), C_n(w) is the n^th order Chebyshev polynomial, e is the ripple factor and w is the frequency normalized to the cutoff frequency w_c. With this response Takahasi derived explicit formulas for matching with these networks.

To apply Takahasi's results on the modeled impedances (loads), a bandpass transformation on the LC ladder networks is essential so that the loads can be absorbed as part of the network. At a certain bias point, the GaAs FET series R_iL_iC_i input impedance can represent the optimum noise source impedance or impedance to achieve a certain associated gain. In this example, the series R_iL_iC_i impedance of the GaAs FET model represents the optimum noise impedance, therefore, the goal of input matching network is to match this impedance to 50 Ω source for lowest noise figure.

Similarly, the output impedance of the GaAs FET is matched to 50 Ω for the gain represented by the output impedance. The output-matching network can be designed for maximum gain or to compensate for the gain rolloff of the device. Matching is possible if the gain bandwidth constraints for the input and output matching networks are satisfied.

Since the input and output impedances of the MESFETs are high and different, ideal transformers are introduced in the design, which are then replaced by equivalent ‘T’ or ‘pi’ networks. The output of this process ends up with good initial circuit for computer optimization, which further requires several quick iterations to achieve the desired objectives.

The data inputs to the input matching network program are Ri=15.543Ω, Li=0.3488 nH, Ci=1.303 pF, F1=4 GHz, F2=8 GHz and n=2. By choosing e=0.12, we get K₂=0.95. F1 and F2 are the lower and upper band edge frequencies. Upon using the above data, we get the elements of the input noise-matching network as CP1=0.5853pF, SEL-2=0.5024 nH, SHL-3=0.8498 nH and SEL-4=0.1391 nH. The response of this input matching network can be verified in a 50-ohm system. The complete amplifier response with lumped elements without optimization is shown in Figure 1. This verifies the validity of the design and the computer program. The amplifier results with distributed elements and post-optimization, using Genesys V8, are shown in Figure 2. The targeted optimized results show a gain of 11 ± 0.3 dB and noise figure of less than 1.2 dB in the entire frequency band. The optimized noise figure is satisfactory considering that the maximum optimum noise figure of the device itself is 0.8 dB in the frequency band.

Because of the high input and output impedances of the GaAs FET, the input and output VSWR of the amplifier is poor and can be improved by incorporating other techniques, including balancing the single-ended amplifier with 90° hybrids such as Lange couplers.

1. D. J. Mellor, “Improved Computer-Aided Synthesis Tools for the Design of Matching Networks for Wideband Microwave Amplifiers,” IEEE Transactions on Microwave Theory and Techniques, vol., MTT-34, No.12, December 1996.

2. H. Takahasi, “On the Ladder Type Filter Network with Chebyshev Response,” J. Inst. Elec. Commun. Engrs., Japan, vol. 34, No. 2, pp. 65-74, 1951.

3. L. Weinberg and P. Slepian, “Takahasi's Results on Chebyshev and Butterworth Ladder Networks,” IRE Trans. Circuit Theory, vol. CT-7, pp. 88-101, 1960.

4. Tri. T. Ha, “Solid-state Microwave Amplifier Design,” A Wiley Inter Science Publication, John Wiley and Sons Inc.1981.

Ashok Nawarange is an RF consultant. His e-mail address is: Aooola@aol.com.