I have the following BJT based current mirror
for part a, I used an approximate analysis illustrated below: \begin{equation} V_{B2}=0.7V=V_{C2}\\V_{BE1}=V_{B1}-V_{C2\:}\rightarrow V_{B1}=0.7+0.7=1.4=V_{C1}\\V_{BE3}=V_{B1}-V_{E3\:}\rightarrow V_{E3}=1.4-0.7=0.7V\\R=\frac{V_{E3}}{I_{E3}}=\frac{0.7V}{10\mu A}=70K\Omega \end{equation} Now for part b, to find the output resistance, I must use the small signal equivalent circuit. That is done by opening the current source and attaching a test voltage vo to the output. The equivalent circuit is displayed below:
simulate this circuit – Schematic created using CircuitLab
Here is my mathematical analysis for the small signal circuit: \begin{equation} v_o=r_o3\left(i_o-g_{m3}v_{\pi 3}\right)+R\left(i_o-g_{m3}v_{\pi 3}+\frac{v_{\pi 3}}{r_{e3}}\right)\\re-arranging:\\v_o=i_o\left(r_{o3}+R\right)-\left(g_{m3}\left(r_{o3}+R\right)-\frac{R}{r_{e3}}\right)v_{\pi 3} \end{equation} Now using the v_pi3 loop of the emitter of Q1 and R we get: \begin{equation} v_{\pi 3}+R\left(i_o-g_{m3}v_{\pi 3}+\frac{v_{\pi 3}}{r_{e3}}\right)=0\\re-arranging:\\v_{\pi 3}=\frac{R}{Rg_{m3}-\frac{R}{r_{e3}}-1}i_o \end{equation} Now substituting we get the final Ro as: \begin{equation} \frac{v_o}{i_o}=R_o=r_{o3}+R-\left[g_{m3}\left(r_{o3}+R\right)-\frac{R}{r_{e3}}\right]\left(\frac{R}{Rg_{m3}-\frac{R}{r_{e3}}-1}\right)\\now:\\r_{o3}=r_o=\frac{V_A}{I_o}=\frac{40V}{10\mu A}=4M\Omega\\r_{e3}=r_e=\frac{\alpha V_T}{I_o}=\frac{\left(0.99\right)\left(25mV\right)}{10\mu A}=2.5K\Omega\\g_{m3}=g_m=\frac{I_o}{V_T}=\frac{10\mu A}{25mV}=0.4mS \end{equation} Substituting the corresponding values, I get Ro to equal: \begin{equation} R_o=116M\Omega \end{equation} Now I tried to verify my results, so I decided to simulate my circuit using LTSpice. Here is my schematic:
Below are my DC operating point results, they do seem close to my hand calculated values:
Now utilizing the AC analysis to find Ro, I get that Ro=83M Ohms as displayed below:
Can somebody please tell me why am getting such a big difference between my calculated and simulated values for Ro?? Please help me figure out if there is something wrong with my analytical equations or the way I set up my circuit in LTSpice. Thank you for your help in advance.