An Introduction to Broadband Impedance Transformation for RF Power Amplifiers

Introduction When analytically defining radio frequency circuits, a common approach incorporates admittance or impedance. Admittance, which is symbolized by Y, is defined in terms of conductance G and an imaginary susceptance component, jB. Admittance is often useful when defining parallel elements in a network and is expressed by the complex algebraic equation Y = G + jB. Impedance, the mathematical inverse of admittance, is symbolized by Z and consists of a resistive component R in units of ohms and a reactive or imaginary component jX. Together in a series complex expression they define impedance as Z = R + jX. Impedance in this rectangular form is often used in industry to define a power device’s optimal source or load. For linear systems, the condition for maximum power transfer is obtained when the impedance of the circuit receiving a signal has an equal resistance and an opposite reactance of the circuit sending the signal. In the mathematics of complex variables, this relationship is known as the complex conjugate. The complex conjugate of a complex number is obtained by simply reversing the sign of the imaginary part. Here Z* denotes the complex conjugate of Z; thus, for linear systems the condition for maximum power transfer is when ZLoad = ZSource*, or: ZL = ZS*. As the frequency of operation changes for ZS, relative to its parasitics, the value of the resistive component can substantially change as well as the value of the imaginary component. Transforming a standard system impedance to present a driving point load impedance ZL that maintains a complex conjugate relationship to the source impedance change over frequency is the most challenging aspect of broadband design. Note: The linear condition for maximum power transfer is often traded for other performance parameters such as efficiency or gain. For this tradeoff the load impedance will not hold a conjugate relationship; however, the challenge of maintaining a load for this performance parameter over a broadband will generally remain the same.