Help with output impedance of a circuit
We can use a small-signal analysis to find the output impedance. We also recognize the bootstrap capacitor \$C_2\$.

But we are now interested in finding the output resistance. 

   

After some further simplification, we get this equivalent circuit.  







simulate this circuit &ndash; Schematic created using CircuitLab

We can see that: 

$$V_{O} = (\frac{I_E}{\beta +1}+I_{R_3})R_{sig} + I_E\: r_e$$

$$R_{OUT} = \frac{r_e (R_3 + R_{sig}) + \frac{R_3 R_{sig}}{\beta +1}}{R_B + r_e}||R_E$$

Now for your circuit, we need to find the quiescent current. 

$$I_E = \frac{4.5V - 0.7V}{2k\Omega + \frac{20k\Omega}{\beta +1}} \approx 1.728mA...1.8mA $$ if we assume that \$\beta = 100..200\$ 

Thus now we can find \$r_e\$ we have \$r_e \approx \frac{26mV}{I_E} \approx 15\Omega...14\Omega \$  

So, we have all we need to find output resistance. 

\$R_E = R_1||R_2||R_4 \approx 1.67k\Omega\$

And 

\$R_{out} \approx 117\Omega\$ for \$\beta = 100\$

Or 

\$R_{out} \approx 74.2\Omega\$ for \$ \beta = 200\$