In this Instructable you will be doing calculations and simulations for Op-Amp touch LED circuit. The LED is supposed to turn on when the two terminals are connected. This circuit might not have been fully tested in practice.

### Supplies:

PSpice simulation software.

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## Step 1: Calculations

The input resistance of operational amplifier is very high. The difference between terminal 2 and terminal 3 voltages is very low.

The voltage at terminal 3 of OpAmp is almost 5 volts. V3 = Vs * R1 / (R1 + Rhuman) = 5 V * 1 Meg / (1 Megohm + 100 kohm) = 4.54 V. If the human skin resistance is 1 Megohm then the voltage at terminal 3 will be only 2.5 V.

In this circuit, the two LEDs are modelled as three general-purpose diodes because each diode has a 0.7 volts voltage across it.

The real op-amp might have as much as 2 V saturation limit. Thus the maximum output can be no more than Vs - 2 V = 3 V. This means that the two LEDs might not turn on because they require 4 V minimum total (2 V each). However, if the saturation voltage is only 0.5 V then both LEDs will turn on. (Vs - Vsat - Vled) / Rd = 0.5 V / 68 ohms = 7.35 mA. LED are supposed to be operating at 10 mA. However, if a modern Op-Amps of zero saturation voltage is used then the current across the LEDs will be (Vs - Vled) / Rd = (5 V - 4 V) / 68 ohms = 14.71 mA which is well above 10 mA and might burn the LEDs.

Then we do the noise frequency calculations: fmax = 1 / (2 * pi * 10 pF * 1 Megohm) = 1.592 kHz (assuming the noise is a current source). You can also calculate the time constant: Rhuman*R1/(Rhuman+R1)*C1 = 9.09 microseconds. In 5 time constants (45.45 microseconds) the capacitor, C1 is fully charged. However, this time constant would be ten times greater is the human skin resistance is 10 times greater. If the noise is a voltage source then the maximum frequency will be: fmax = 1/(2*pi*Time Constant) = 17.509 kHz.

## Step 2: Simulations

Simulations show that there almost is no saturation voltage. The minimum voltage does not fall below about 2 V for the following reasons:

- minimum saturation voltage,

- offset currents,

- offset voltages,

- bias currents,

- bias voltages.

Those are the non-ideal characteristics of practical op-amps.

Modern op-amps have higher bandwidth and lower offset/bias voltages and currents.

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