---+ Resistor Selection

This page is a reference guide for the selection of the resistor for connections J1 and J3 on the Cryo Electronics board. The choice of resistor will select the gains in the sense and drive circuit. Our goal is to optimize the signal's dynamic range (to maximize signal-to-noise, without railing the amplifier.)

Drive Circuit Gain (J1)

the necessary equations are...

The gain of the Op-Amp LT1168CS8-- Gain=(49.4k/Rg)+1

Calculating the current I=Vin/(Gain*100k)

ADC=2.5/2^24

RTD (Resistive Thermometer)

In order to not rail the amplifier Vin can not be larger than 1.25 volts but the ADC gives us sensitivity at 149nV so we do not need to be anywhere near 1 volt in fact ranges of .1 V is just fine.

For the RTD's in our cryostat i.e. Cernox CX-1010 the necessary excitation voltage is 63 micro volts and the resistance of the RTD is 1k (this is for the typical temperature range of .5-1k) this means that we want a current of 63 nA. however at the temperature range of .1 Kelvin the excitation changes to 20 micro volts and the resistance changes to 10k this implies we want just 2nA at this temperature. splitting the difference it makes sense to send 10nA

What this tells us is that the 100k resistor in the current equation has a potential difference of 1mv we can then set this (relatively arbitrarily) to have a gain of 100 and we then have enough wiggle room to avoid railing the amplifier and also have the sensitivity we want on the adc

Then setting 100 as the gain in the gain equation we find 100=(49.4k/rg)+1=> rg= 500 ohms

Diode

For Diode we want a constant excitation of 10 micro amps. This excitation implies a voltage difference of 1 volt across the 100k resistor. Therefore, the gain should be one and the resistor should be left open.

Sense Circuit Gain (J3)

For the Sense Circuit, the gain equation is the same. We use the same Op-Amp and again we have 1.25 volts until we rail the amplifier.

RTD (Resistive Thermometer)

We want to have the ability to go from .1k to 1k where the resistance range is 10k ohms to 1k ohm this implies that at 1k we can not be producing more than .1 volts otherwise we risk railing the amplifier at the other end of the spectrum this implies with a bias of 10nA and a resistance of 10 k ohms we have a potential of .1 mV this implies a gain of 500 is not in danger of railing the amplifiers.

Using 500 in the gain equation we find 500=(49.4k/rg)+1=> rg= 100 ohms

Below is a graph of the adc counts as a function of temperature with a gain of 500 the functional relationship is ADC=(1*10^-9)*((2^24)/2.5)*(T^(-1.13)+800)

-- Pete Dahlberg (this page should be checked by someone with an electronics background)

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This topic: CryoElectronics > DigitalFMux > ResistorSelectionForCryoBoard Topic revision: r7 - 2014-02-28 - GraemeSmecher

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