Theoretical analysis of amplifier circuit
I did the DC analysis by hand:




Summary:

Theoretical:

Ib = 5.963uA

Ic = 895uA

Ie = 900uA

Vce = 7.362V

Spice:

          --- Operating Point ---
V(n002):     6.71675     voltage
V(n005):     0.895875    voltage
V(n006):     0.248847    voltage
V(n001):     12  voltage
V(n004):     0   voltage
V(n003):     1.47768e-014    voltage
Ic(Q1):  0.0011241   device_current
Ib(Q1):  7.02464e-006    device_current
Ie(Q1):  -0.00113112     device_current
I(C2):   6.71675e-019    device_current
I(C1):   -8.95875e-020   device_current
I(R5):   -6.71675e-019   device_current
I(R4):   0.000497708     device_current
I(R3):   0.000504733     device_current
I(R2):   0.00113112  device_current
I(R1):   0.0011241   device_current
I(V2):   -0.00162883     device_current
I(V1):   8.95875e-020    device_current


Then the AC analysis:

Gain:


Summary:

Theoretical:

Voltage Gain: -17.6

Spice:


This gives you the -3db points:

f-low: ~= 500Hz

f-high: ~= 24MHz

Comments:

As you can see the theoretical and Spice DC analyses match closely. Spice differs since it takes many more factors into consideration.