LDR VCA análisis

Assumptions:

• Los dos opamps son ideales (A_d=∞, A_cm=0, I_in=0).
• Los dos LDRs son iguales.
• Los dos LDRs están expuestos a la misma cantidad de luz desde el LED.
• Los LDRs están escondidos de la luz ambiente.

Because I_in=0, all of the current from the control input continues through the bottom LDR, to the -15V supply.

V_control / 10k = 15 / R_LDR, so
R_LDR = (15 * 10k) / V_control
R_LDR = 150k / V_control (eq 1)

We assume the two LDRs have the same resistance at all times.

The audio path is composed of two gains, cascaded.

A_v1: The voltage gain from the AUDIO INPUT terminal to the left terminal of the upper LDR.
A_v2: The voltage gain from the left terminal of the upper LDR to the OUTPUT terminal, assuming the output is unloaded.

A_v1 = -1 * 150k / 150k
A_v1 = -1

A_v2 = -1 * 150k / R_LDR (eq 2)

Substituting the expression for R_LDR from (eq 1) into (eq 2), we get:

A_v2 = -150k / (150k / V_control), or
A_v2 = -V_control

Therefore,

A_total = A_v1 * A_v2
A_total = -1 * -V_control
A_total = V_control