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Entry  Fri Sep 8 03:29:00 2017, Kevin, DailyProgress, TempCtrl, Heater Circuit HeaterCircuit.pdfTop.jpgFront.jpgBack.jpgTestSetup.jpg
    Reply  Thu Jan 11 14:24:11 2018, awade, DailyProgress, TempCtrl, Lowing can heater effective resistance HeaterConfigs.pdfMaxHeatingPower_CurrentAndVoltageLimited.pdf
       Reply  Thu Jan 11 19:15:43 2018, awade, DailyProgress, TempCtrl, Follow up: Lowing can heater effective resistance HeaterConfigs_badconfig20180111.pdf
Message ID: 2043     Entry time: Thu Jan 11 14:24:11 2018     In reply to: 1903     Reply to this: 2045
Author: awade 
Type: DailyProgress 
Category: TempCtrl 
Subject: Lowing can heater effective resistance 

For the vacuum can heater, we are limited in the heater driver max power by the positive supply rail voltage and the maximum current permissible through the sense resistor. The 54 Ω of the can heater means that for 0.44 A of drive current, the drop across the heater is 24 V, the maximum voltage available to the circuit.  Thus there is a limit to total heating of 9.77 W, accounting for sense resistor and MOSFET voltage drop.

The present resistor configuration is illustrated in the attachment (Configuration A).  Heating is proportional to area. With 38 Ω + 70 Ω in two parallel resistive circuits the current is the same through all resistive elements: this deliverers the most even heating per unit are across the can. This is at the penalty of lower heating.

Max power is given by 

P_\textrm{max} = \left(\frac{V_\textrm{cc}-V_\textrm{FET,GS}}{R_\textrm{load}+R_s}\right)^2 R_\textrm{load}

Where Vcc is max supply voltage, VFET,GS is the voltage drop from gate to source of the FET, Rs is the sensor resistor (1 Ω, 3W, 50ppm/K in this case) and Rload is the total resistance of the heaters on the can. I've plotted the maximum power verses load taking the larger of heater load voltage drop or max current as the limiting factor for a few choices of max current. This is attached below.

Of the three configurations of resistive heater hookup the option C provides the most heating within the voltage limits of the circuit but with 3.8 times more heating at the ends compared to the middle.  The time constant on heating is probably long enough for the steal to conduct without too much temperature gradient.  Configuration B is a compromise with relatively even heat with about 21 W heating.

Previous measurements of the heating requirements showed that 24.5 W was enough to hold the vacuum can at stead state 45 C.  Heating of 10 W is sufficient to reach 30 C easly. We would like the option to heat up to 40 C, so configuration B in the attached schematic is enough but doesn't leave much overhead.

For now I will just configure the heaters to all be in parallel (configuration C).

Self heating and drift

We want to avoid driving the sense resistor towards it maximum current, it will self heat and drift by

\Delta P_\textrm{Drift} = -2 \left(\delta R_s/R_s \right ) \times P_\textrm{heater}

to first order.  Where the fraction is the ppm/K expected change and P_\textrm{heater} is the average set point heating power. For the resistor used (1Ω) this temperature coefficient is 50ppm/K with a maximum power dissipation of 3 W.  From some previous tests running the the heater driver at 2 A I found the sense resistor seemed to heat up by about 3-5K (just by touch feel).  This could mean that a 20 W heater setting could self heat the circuit to a offset of 10 mW. We want to limit current to some reasonable value, choose 1.5 A for now.

Attachment 1: HeaterConfigs.pdf  23 kB  Uploaded Thu Jan 11 17:04:05 2018  | Hide | Hide all
HeaterConfigs.pdf
Attachment 2: MaxHeatingPower_CurrentAndVoltageLimited.pdf  18 kB  Uploaded Thu Jan 11 17:16:16 2018  | Hide | Hide all
MaxHeatingPower_CurrentAndVoltageLimited.pdf
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