Error analysis of the CMOS based soft gate for analog turbo decoder

In This work we derive an error model for the modified Gilbert multiplier, soft gate. Such multiplier is the basic building block of an analog turbo decoder. Error in the soft gate impacts the performance of the decoder. Our purpose is to derive the equation that allows to minimize this error. The error model describes variation at the multiplier output and is derived based on the mismatch in the individual transistors. We are looking at the CMOS process where the transistors are operating in the subthreshold. The mismatch is described as the variation in current factor and threshold voltage of the individual transistors. These parameters depended on circuit production process and therefore the model allows to study the impact of the process parameters to the error in decoding. As it turns out the soft gate error depends on the working point of the multiplier. In weak inversion the relative impact of the individual transistor mismatch error to the soft gate output error is higher than in strong inversion.