I am trying to compare theoretical results with the simulation of the following amplifier.
The respective values are $$V_\mathrm{CC} = 12\,\text{V}, R_\mathrm{B} = 470\,\text{k}\Omega, R_\mathrm{C} = 2\,\text{k}\Omega, R_\mathrm{load} = 8\,\text{k}\Omega, C_1 = C_2 = 22\,\mathrm{nF}, \beta = 100,$$ where β is the DC current gain.
Putting together the basic equations, we have \begin{equation} I_\mathrm{C} = \beta I_\mathrm{B} = \beta\left(\frac{V_\mathrm{CC} - V_\mathrm{BE}}{R_\mathrm{B}}\right) = 100\left(\frac{12 - 0.7}{470\cdot10^{3}}\right)\approx 2\,\mathrm{mA}, \end{equation} transconductance \begin{equation} g_\mathrm{m} = \frac{I_\mathrm{C}}{V_\mathrm{T}} = 80\,\mathrm{mS}, \end{equation} and resistance \begin{equation} r_\pi = \frac{\beta}{g_\mathrm{m}} = 1.25\,\mathrm{k}\Omega. \end{equation}
Using these values to establish the hybrid-pi model, we get an auxiliary schematic.
I am interested in voltage gain, which should be the calculation equal to \begin{equation} A_\mathrm{u} = \dfrac{v_\mathrm{out}}{v_\mathrm{in}} = \dfrac{-i_\mathrm{C}\dfrac{R_\mathrm{C}R_\mathrm{load}}{R_\mathrm{C} + R_\mathrm{load}}}{v_\mathrm{BE}} = -\dfrac{g_\mathrm{m}v_\mathrm{BE}\dfrac{R_\mathrm{C}R_\mathrm{load}}{R_\mathrm{C} + R_\mathrm{load}}}{v_\mathrm{BE}} = -g_\mathrm{m} \frac{R_\mathrm{C}R_\mathrm{load}}{R_\mathrm{C} + R_\mathrm{load}} = -128. \end{equation}
Trying to compare this to a simulation, I used LTSpice with the following schematic
The selected transistor is 2SC4083 with the SPICE model
.model 2SC4083 NPN(Is=1.0000E-15 Bf=93.539 Vaf=100 Ikf=31.168E-3 Ise=175.74E-15 Ne=2.2255 Br=4.1981 Var=100 Ikr=1.5983 Isc=25.314E-15 Nc=1.5008 Nk=.20045 Rb=10 Rc=3.8727 Cje=2.3961E-12 Mje=.21324 Cjc=1.1921E-12 Mjc=.1498 Tf=34.367E-12 Xtf=26.703 Vtf=21.035 Itf=.73447 Tr=45.521E-9 Xtb=1.5000 Vceo=11 Icrating=0.05 mfg=Rohm)
I admit that this selection might be the potential problem, because I chose it based on the DC gain being close to 100.
Finally, there is my problem. I wanted to compare the theoretical gain to the simulation. The input voltage source is \begin{equation} v_\mathrm{in}\left(t\right) = 0.1\sin{\left(2\pi 100 t\right)}. \end{equation}
When I run the simulation, I receive the following plot. Blue is the input voltage, and the green one is the output voltage.
The output signal is attenuated and not inverted. This goes significantly against the theoretical calculations. What might be the source of the error?
