Modeling Rf Circuits for Systems Analysis 6. Conclusions and Future Work 5.2 Transistor-level Test Circuit

6 MIMO model. The non-linear part of the cascade model can scale the linear filter's response depending on bias but it can not move the poles and zeros. In contrast, the K-model can move the poles and zeros for bias. The K-model is a behavioral model and consequently not exact. However, it is an improvement over linear models, memoryless non-linear models, and cascaded combinations of linear filters and memoryless non-linearities. Simulations of two different test circuits show the modeling error is about 10% for input excursions well into the saturation region of the DC transfer curve. The first test circuit was very simple and composed mostly of behavioral blocks implemented in AHDL. The second test circuit was composed of device models and used very little AHDL. Aside from validating the K-model, the two test circuits demonstrate that the K-model can be used to extract a system-level model from any mix of behavioral and device models. This implies the K-model can be used during any phase of the receiver's design to see if the present concept will work in the larger system. We used Alta's DSP tool, SPW, to simulate the K-model. The key SPW block read in transfer functions extracted using SpectreRF then applied an IFFT to compute impulse responses. To simulate a transfer function, SPW convolved the sampled input with the sampled impulse response. There are other ways to simulate the transfer functions. One could apply the FFT to chunks of input data, multiply the FFT by the transfer function, then apply an IFFT to return to the time domain. However, that approach does not work well in feedback loops because the output is delayed by the length of a data chunk. Another approach is to fit rational transfer functions to the measured transfer functions. The rational transfer functions can be decomposed into pole-residue forms which can then be simulated with recursive convolu-tion [8]. Recursive convolution is very fast. The first step is to make sure the rational transfer function approach is as good as or better than the FIR filter approach. We implemented a K-model of the simple test circuit with rational transfer functions and simulated it in SpectreRF. Test results were not noticeably different from SPW test results. We are still working on applying a rational transfer function implementation of the K-model to the large test circuit. Along with increased simulation speed the rational transfer function approach …