ansu_s
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Hi,
I try to match model of first order sigma delta to spectre simulation results, but they disagree!
First figure attached is first order sigma-delta model (comparator shown as a summing node and noise source N(s)). Can solve to get:
Y = N/(1+H) + H*X/(1+H) where H=K/s
So if K/s >> 1, then:
Y ~ sN/K + X
This says to me that to decrease in-band noise, just increase K, making sN/K smaller.
However, in spectre simulation (using veriloga blocks to implement each mathematical block) with two values of K (1e6 and 100e6), results shown in second attachment. Only difference is in scaling of integrator output. First trace with K=100e6 shows integrator output range of approx -110V->+260V (ideal veriloga components, so large voltages OK). Second trace with K=1e6 shows integrator output range approx -1.1V->2.6V. Third trace shows first_trace/second_trace, and gives values of 100 - so the two are exact scalings of each other. Comparator is only sensitive to crossing points of integrator output and comparator reference, but these are identical for both waveforms. So comparator output is identical for both K values, so sigma-delta modulator does not care about value of K.
But mathematical model shows that increased K should reduce noise - but it makes no difference in simulation! Why is this?
I try to match model of first order sigma delta to spectre simulation results, but they disagree!
First figure attached is first order sigma-delta model (comparator shown as a summing node and noise source N(s)). Can solve to get:
Y = N/(1+H) + H*X/(1+H) where H=K/s
So if K/s >> 1, then:
Y ~ sN/K + X
This says to me that to decrease in-band noise, just increase K, making sN/K smaller.
However, in spectre simulation (using veriloga blocks to implement each mathematical block) with two values of K (1e6 and 100e6), results shown in second attachment. Only difference is in scaling of integrator output. First trace with K=100e6 shows integrator output range of approx -110V->+260V (ideal veriloga components, so large voltages OK). Second trace with K=1e6 shows integrator output range approx -1.1V->2.6V. Third trace shows first_trace/second_trace, and gives values of 100 - so the two are exact scalings of each other. Comparator is only sensitive to crossing points of integrator output and comparator reference, but these are identical for both waveforms. So comparator output is identical for both K values, so sigma-delta modulator does not care about value of K.
But mathematical model shows that increased K should reduce noise - but it makes no difference in simulation! Why is this?
"Applying linear system concepts to a sigma delta provides valuable insight, but is flawed from the outset", presumably as the sigma delta is not a linear system. They also cover the above problem, where they add a gain K to the output of a loop filter before the quantizer. Then they say that this will not affect the operation of the modulator (as per the simulation results above), but it does affect the linear model transfer function, altering the signal and noise transfer functions.