Real (non-ideal) op-amps - textbook query

[discombobulated]

Homework Statement

Hello,

I'm studying real op-amps and looking the inverting amplifier circuit for a non-ideal op amp model. I'm confused as to where one of the equations from the assumption of zero output current came from, as I get a slightly different one.

I've attached the circuit diagram.

Homework Equations

1. From assumption of zero input for ideal, which requires Z_in >> R₁, R₂and v₁ (inverting input) = v_d, and v₂ (non-inverting input) = 0.

I get v_d = [R₁ / (R₁ + (R₂)]v_in + βv₀

The Attempt at a Solution

For the 2_nd assumption of zero output impedance requires Z₀ << R₂

I get the equation: v₀ = A_OLv_d - i₀Z₀

but the book says: v₀ = - A_OLv_d - i₀Z₀

 

[berkeman]

Homework Statement

Hello,

I'm studying real op-amps and looking the inverting amplifier circuit for a non-ideal op amp model. I'm confused as to where one of the equations from the assumption of zero output current came from, as I get a slightly different one.

I've attached the circuit diagram.

Homework Equations

1. From assumption of zero input for ideal, which requires Z_in >> R₁, R₂and v₁ (inverting input) = v_d, and v₂ (non-inverting input) = 0.

I get v_d = [R₁ / (R₁ + (R₂)]v_in + βv₀

The Attempt at a Solution

For the 2_nd assumption of zero output impedance requires Z₀ << R₂

I get the equation: v₀ = A_OLv_d - i₀Z₀

but the book says: v₀ = - A_OLv_d - i₀Z₀

I think it's just the sign of the input voltage. Remember that the - terminal is at the top, and the + terminal is at the bottom, as drawn. Which way is the Vd defined?

Also, there is a typo in your 2nd sentence. Are you referring to input current or output impedance when you said "assumption of zero output current"?