Microwave Engineering Europe - December 2008 - (Page 21) X-PARAMETERS 21 than treated as a small signal in order to accurately predict device behavior. One way of accomplishing this is to include Γ21, the reflection coefficient at port 2 fundamental frequency, in the LSOP resulting in Equation 3. The sums now exclude terms related to A21. Equation 3: extract X-parameters with the Agilent NVNA, model the component in Agilent ADS with Xparameters encapsulated by the PHD component, and design nonlinear circuits and systems with X-parameters in ADS. All the pieces of the nonlinear puzzle have been created, and they now fit together, seamlessly. X-parameters: doing for nonlinear components/systems what Sparameters do for linear components/systems. References [1] http://www.agilent.com/find/nvna [2] D. E. Root et al IEEE Transactions on Microwave Theory and Techniques Vol. 53. No. 11, November, 2005 pp. 3656-3664 [3] J. Verspecht and D. E. Root, in IEEE Microwave Theory and Techniques Microwave Magazine, June, 2006. [4] J. Horn et al in IEEE European Microwave Conference, Amsterdam, October, 2008 [5] G. Simpson et al, IEEE MTT-S ARFTG Conference, Portland, OR, December, 2008 [6] J. Verspecht et IEEE MTT-S International Microwave Symposium Digest, Honolulu, HI, USA, June 2007 A longer more detailed version of this article and the author details can be found at www.mwee.com. In practice, this can be accomplished by using a fundamental load tuner together with an NVNA to measure X-parameters over the entire range of load conditions of interest [5]. The resulting set of load-dependent Xparameters are accurate over the entire region of measured load conditions. Figure 7 shows a comparison of simulated results from loaddependent X-parameters and independent time-domain load-pull measurements. Modulated signals Although X-parameters are measured under periodic sinusoidal or multi-sine stimulus conditions, they can be used in the Circuit Envelope simulator in Agilent ADS to estimate the response of the device under modulated conditions as well. This allows X-parameters measured under single-tone stimulus to estimate the device response to two-tone or multi-tone stimulus, since the stimulus can be represented as a modulated single-carrier signal. In addition, the response to complex modulated stimulus can be estimated. This allows common figures of merit such as IP3 or ACLR to be estimated even from single-tone X-parameters. Figure 8 shows an example of two-tone and WCDMA modulated simulation results from single-tone X-parameter measurements. X-parameters have been demonstrated to apply to multi-port nonlinear devices such as mixers, and applied to problems including memory affects [6]. Applications of X-parameters to everything from nonlinear transistor modeling, multi-stage amplifier design, nonlinear RF system design, stability analysis of power amplifiers, and amplifier linearization methodologies are sure to follow. Conclusion X-parameters are the supersets of S-parameters, load-pull, and waveform measurements. They unify high-frequency characterization, modeling, and design of nonlinear microwave and RF components and systems. We can measure and Figure 7: Load-dependent Xparameters for a packaged WJ Communications transistor: Top shows a comparison of simulated (blue) and measured (red) delivered power and efficiency contours. Bottom shows a comparison of simulated (lines) and measured (markers) voltage and current waveforms at one specific load (Gamma = 0.383 + j*0.31). Figure 8: PHD components can be used in Envelope simulation to provide estimates of ACPR and IM3 with guaranteed accuracy in the narrow-band limit. Top shows overlay of simulated and measured spectrum under 3GPP WCDMA stimulus at 13 dBm output power, bottom left shows simulated IM3 versus input power, bottom right shows ACLR comparison. Microwave Engineering ● December 2005 ● www.mwee.com http://www.agilent.com/ http://www.mwee.com http://www.mwee.com
For optimal viewing of this digital publication, please enable JavaScript and then refresh the page. If you would like to try to load the digital publication without using Flash Player detection, please click here.