Transconductance Op-amp Compensation

Note The way we have separated the terms of the transconductance op-amp, the pole-at-zero (fpO H3) seems to be dependent only on Cl (no resistance term). However, we could have also clubbed the voltage divider section HI along with H3 (since these are simply cascaded blocks, in no particular order). Then the pole-at-zero would have appeared differently (and also included a resistance term). However, whichever way we proceed, the final result, that is, H, will remain unchanged. In other words, HI, H2, and H3 are just intermediate mathematical constructs in calculating H (with no obvious physical meaning of their own necessarily). That is why the actual pole-at-zero frequency of the entire feedback block is designated as fpO, not fpO H3. 

Example Using a 300 kHz synchronous buck controller we wish to step down 25 V to 5 V. The load resistor is 0.2 Q (25 A). The ramp is 2.14 V from the datasheet of the part. The selected inductor is 5 pH, and the output capacitor is 330 pF, with an ESR of 48 mfi. The transconductance of the error amplifier is gm = 0.3 (units for transconductance are mhos, i.e. ohms spelled backwards). The reference voltage is 1 V. 

We choose our target crossover frequency fcross as 50 kHz. We pick Rf2 = 4 kf2 and Rfl = 1 kf2 based on the voltage divider equation, the output voltage, and the reference voltage. Then 

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There is a practical difficulty involved in using the full-blown transconductance op-amp compensation scheme discussed above — because the pole and zero from HI are not independent. They will even tend to coincide if say Rf2 is much smaller than Rfl (i.e. if the desired output voltage is almost identical to the reference voltage). In that case, the pole and zero coming from HI will cancel each other out completely. Therefore, we can t proceed anymore, because we were counting on the zero from HI to change the open-loop gain from —2, to —1, just in time before it crossed over. 

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