Question Problem 2: For the differential amplifier shown in the following figure, identify and sketch the differential half-circuit and the common-mode half-circuit. Find the differential gain, the differential input resistance, the common-mode gain assuming the resistance Rc have 1% tolerance, and the common-mode input resistance. For these transistors, B=100 and VA = 100 V. +10 V Rc 10 ΚΩ: Re 3 10 ΚΩ Pod R 20 ΚΩ RE w 300 Ω 200 ΚΩ 200 ΚΩ 10.5 mA 0.5 mA

solution please give me like..its really needs to write more questions,,thanks Answer:-Given that \beta=100 and V_{A}=100 \mathrm{~V}Each transisto is biased at E_{E}=0.5 \mathrm{~mA}\begin{array}{l}\text { Each transistou is blased at IE } \\\gamma_{e_{1}}=\gamma_{e 2}=\frac{V_{T}}{I_{E}}=\frac{25 \mathrm{mV}}{0.5 \mathrm{~mA}}=50 \Omega, g_{m}=\frac{1}{\gamma_{e}}=20 \mathrm{mall} \\V_{A}=100 \mathrm{~V} \text { and } I_{E}=0.5 \mathrm{~mA} ; \gamma_{0}=\frac{V_{A}}{I E}=\frac{100}{0.5}=200 \mathrm{k} \Omega\end{array}\rightarrow Differential halt circcit\leftrightarrow common mode halt circutGain A V=\frac{\text { Total Resistance in the collectors }}{\text { rotal Resistance in the enitters }}Ditterential gain A d=\frac{2(R c \| R L / 2)}{2(\gamma e+R E / 2)}=\frac{2(10 \| 10) \mathrm{K}}{2(0.05+0.15) \mathrm{K}}A_{d}=25 \mathrm{~V} / \mathrm{V}Ditterential input resistance Rid\begin{aligned}\text { Rid }=2\left((\beta+1)\left(\gamma_{e}+R E 1_{2}\right)\right) & =2(108)(50+150) \\& =40.4 \mathrm{k} \Omega \\\text { Rid } & =40.4 \mathrm{k} \Omega\end{aligned}\rightarrow common mode gain with R_{C} have (Y, tolesance\begin{array}{r}A_{c M}=\frac{\Delta R C}{R_{C}} \cdot \frac{R_{C}}{R_{E E}}=\frac{\Delta R_{C} \cdot R_{C}}{R_{C} R_{E E}}=\frac{10}{200}(0.01) \\=5 \times 10^{-4} \\A_{C M}=5 \times 10^{-4} \mathrm{~V} / \mathrm{V} \quad\left[\because \frac{\Delta R_{C}}{R_{C}}=1 \%=0.01\right]\end{array}\rightarrow common mode input resistance Ricm:\operatorname{Ricm}=(\beta+1)\left[\frac{r_{e}}{2}+\left(\frac{R_{E E}}{2} \| \frac{r_{0}}{2}\right)\right]\begin{array}{l}=(101)\left(25+\left(\frac{200 \mathrm{k}}{2} \mid 1 \frac{200 \mathrm{k}}{2}\right)\right. \\R_{i c m}=50.525 \mathrm{~m} \Omega\end{array} please dont forget to give like.. if u have any doubts..please comment me,,thanks ...