magician13134
New Member
Hi everyone, I've got a homework problem that's turning out to be quite difficult. We've been given an inverting opamp circuit and told to use the op-amp equivalent circuit to derive an expression for the gain, V_out/V_S.
**broken link removed**
(In this image, taken from Wikipedia, they use V_S instead of V_CC, we use V_S as the voltage connected to the negative terminal)
This is the circuit we're given
**broken link removed**
Again, V_in = V_S and R_in = R_S, but they can be called whatever you want.
Then we're asked to obtain an expression for the closed loop gain, G = V_out/V_s ONLY in terms of R_s, R_in (internal), R_out (internal), R_Load (not shown in the circuit, it simply goes from V_Out to ground), R_F and A (the amplification of this specific op-amp). I tried to use KCL at node n (negative op-amp terminal) and at V_Out, which is what he showed us in class, and I got two equations but I can't seem to get V_Out/V_S in only those terms, I have other terms like V_n (voltage at the negative terminal), V_p (voltage at the positive terminal, but that equals 0, right?).
Here are the equations I got:
[LATEX](V_n-V_s)/R_s + (V_n-V_p)/R_i+(V_n-V_o_u_t)/R_f=0[/LATEX]
[LATEX](V_o_u_t-A(V_p-V_n))/R_o_u_t + (V_o_u_t-V_n)/R_F+V_o_u_t/R_L=0[/LATEX]
Assuming V_p = 0:
[LATEX](V_n-V_s)/R_s + V_n/R_i+(V_n-V_o_u_t)/R_f=0[/LATEX]
[LATEX](V_o_u_t-A*V_n)/R_o_u_t + (V_o_u_t-V_n)/R_F+V_o_u_t/R_L=0[/LATEX]
But that still leaves me with a V_n that I can't seem to get rid of and I can't for the life of me do the algebra to solve for V_out/V_s. Remember, this op-amp is NOT ideal, so you cannot use infinity or 0 for any of the values.
Can anyone please help me?
Thank you!
**broken link removed**
(In this image, taken from Wikipedia, they use V_S instead of V_CC, we use V_S as the voltage connected to the negative terminal)
This is the circuit we're given
**broken link removed**
Again, V_in = V_S and R_in = R_S, but they can be called whatever you want.
Then we're asked to obtain an expression for the closed loop gain, G = V_out/V_s ONLY in terms of R_s, R_in (internal), R_out (internal), R_Load (not shown in the circuit, it simply goes from V_Out to ground), R_F and A (the amplification of this specific op-amp). I tried to use KCL at node n (negative op-amp terminal) and at V_Out, which is what he showed us in class, and I got two equations but I can't seem to get V_Out/V_S in only those terms, I have other terms like V_n (voltage at the negative terminal), V_p (voltage at the positive terminal, but that equals 0, right?).
Here are the equations I got:
[LATEX](V_n-V_s)/R_s + (V_n-V_p)/R_i+(V_n-V_o_u_t)/R_f=0[/LATEX]
[LATEX](V_o_u_t-A(V_p-V_n))/R_o_u_t + (V_o_u_t-V_n)/R_F+V_o_u_t/R_L=0[/LATEX]
Assuming V_p = 0:
[LATEX](V_n-V_s)/R_s + V_n/R_i+(V_n-V_o_u_t)/R_f=0[/LATEX]
[LATEX](V_o_u_t-A*V_n)/R_o_u_t + (V_o_u_t-V_n)/R_F+V_o_u_t/R_L=0[/LATEX]
But that still leaves me with a V_n that I can't seem to get rid of and I can't for the life of me do the algebra to solve for V_out/V_s. Remember, this op-amp is NOT ideal, so you cannot use infinity or 0 for any of the values.
Can anyone please help me?
Thank you!