A series-shunt discrete amplifier uses a loaded open-loop DC gain A=640 V/V that is…

A series-shunt discrete amplifier uses a loaded open-loop DC gain \(A=640\,\mathrm{V/V}\) that is known only to \(\pm 20.0\%\) (uniform, independent of the resistors). The feedback divider is \(R_1\) from output to tap and \(R_2\) from tap to ground, with \(\beta=R_2/(R_1+R_2)\) and intended DC closed-loop gain \(1/\beta=8.00\). The designer may use E96 \(1.00\%\) resistors or E24 \(5.00\%\) resistors. Choose a pair \((R_1,R_2)\) from the E96 series (preferred values \(1.00,1.02,1.05,\ldots,9.76\) times a decade) with both resistors between \(1.00\,\mathrm{k}\Omega\) and \(100\,\mathrm{k}\Omega\) inclusive that realises \(\beta\) with zero nominal error, and a pair from the E24 series (\(1.0,1.1,1.2,1.3,1.5,1.6,1.8,2.0,2.2,2.4,2.7,3.0,3.3,3.6,3.9,4.3,4.7,5.1,5.6,6.2,6.8,7.5,8.2,9.1\) times a decade) in the same range that minimises the absolute nominal error of \(1/\beta\) from \(8.00\). For each pair, using worst-case independent resistor corners at the stated tolerance and independent \(A\) corners at \(\pm 20.0\%\), compute the extreme values of closed-loop DC gain \(A_f=A/(1+A\beta)\) and the extreme values of the DC desensitivity \(1+A\beta\). An unmodelled output pole at \(1.50\,\mathrm{MHz}\) exists in \(A(s)=A/(1+s/\omega_p)\) with \(\omega_p=2\pi\cdot 1.50\times 10^6\,\mathrm{rad/s}\) and the DC \(A\) of each corner; compute PM at the resistor-and-\(A\) corner that minimises PM for each resistor family. Decide whether the E96 choice keeps every \(A_f\) within \(2.00\%\) of \(8.00\) and \(\mathrm{PM}\ge 60.0^\circ\), and whether the E24 choice does so as well.

\(1/\beta=8\) is \(R_1/R_2=7\). Search E96 and E24 for a ratio of 7 inside \(1\,\mathrm{k}\Omega\)–\(100\,\mathrm{k}\Omega\).