Adjoint network method applied to the performance sensitivities of microwave amplifiers

Abstract

This work focuses on the performance sensitivities of microwave amplifiers using the "adjoint network and adjoint variable" method, via "wave" approaches, which includes sensitivities of the transducer power gain, noise figure, and magnitudes and phases of the input and output reflection coefficients. The method can be extended to sensitivities of the other performance measure functions. The adjoint-variable methods for design-sensitivity analysis offer computational speed and accuracy. They can be used for efficiency-based gradient optimization, in tolerance and yield analyses. In this work, an arbitrarily configured microwave amplifier is considered: firstly, each element in the network is modeled by the scattering matrix formulation, then the topology of the network is taken into account using the connection scattering-matrix formulation. The wave approach is utilized in the evaluation of all the performance-measurement functions, then sensitivity invariants are formulated using Tellegen's theorem. Performance sensitivities of the T-and ⌸-types of distributed-parameter amplifiers are considered as a worked example. The numerical results of T-and ⌸-type amplifiers for the design targets of noise figure F req ‫؍‬ 0.46 dB N 1,12 and V ireq ‫؍‬ 1, G Treq ‫؍‬ 12 dB N 15.86 in the frequency range 2-11 GHz are given in comparison to each other. Furthermore, analytical methods of the "gain factorisation" and "chain sensitivity parameter" are applied to the gain and noise sensitivities as well. In addition, "numerical perturbation" is applied to calculation of all the sensitivities.

Adjoint sensitivity analysis of the T, Π, and L types of microstripline low noise amplifiers

“…In this work as a study case, performance sensitivities of the T, Π, and L types of microstrip LNAs with the same design target parameters of maximum gain and input reflection coefficient |Γ in | = 0.3 are given along the operation bandwidth of 10-18 GHz, and comparisons are also made NP and CSM Figure 11. (a) Noise sensitivities of the microstrip amplifiers with respect to the input matching circuit's lengths 1-3. (b) Noise sensitivities of the microstrip amplifiers with respect to the input matching circuit's widths [1][2][3] .…”

“…Considering a microwave circuit built by arbitrarily configured 'm' multiport, in order to analyze this circuit in terms of the wave variables a, b, we must have the following: (i) scattering matrix S (k) of each multiport and reflection coefficients for the indepedent generators and loads; (ii) connection matrix (Γ ) describing the topology of the circuit. Thus, we can express the first feature as where S (1) , S (2) ,….. S (m) are the scattering matrices of the multi-ports or reflection coefficients of the independent generators and loads; the vectors a (1) , a (2) ,……. a (m) ; b (1) , b (2) ,…….…”

“…Thus, we can express the first feature as where S (1) , S (2) ,….. S (m) are the scattering matrices of the multi-ports or reflection coefficients of the independent generators and loads; the vectors a (1) , a (2) ,……. a (m) ; b (1) , b (2) ,……. b (m) and c (1) , c (2) , …….…”

“…a (m) ; b (1) , b (2) ,……. b (m) and c (1) , c (2) , ……. c (m) 'represent incoming, outgoing, and impressed waves related to these elements', respectively.…”

“…In this work, it is aimed to study the sensitivity performance of microstrip amplifiers, with respect to the matching microstripline width w s and length ℓ s depending upon the position and the configuration types, using adjoint network method (ANM) with wave approach for different types of matching networks for responds of the gain G T , noise figure F, input Γ in , and output Γ out reflection of the amplifier in [1]. Design target space solution of the amplifier is obtained in [2], and the results for performance gradients and their applications are given in [3]. In Gunes F and Altunc S (2014) [3], gain gradients are provided using gain factorization and chain sensitivity matrix method, and this work is extended to any performance measure function expressed in terms of wave variables for any configuration type of the amplifier later in Dobrowolski A (1998) [1] using adjoint network and adjoint variables.…”