TEC heat load and required ΔT for a laser diode module

Enter the laser's drive point, the module's thermal path and the TEC's maximum ratings. The calculator adds up the heat the TEC must pump, finds the TEC current, voltage and hot-side heat at the required temperature difference, iterates the heat-sink temperature rise, and checks the load against the TEC's capacity at that temperature difference.

Inputs

Laser diode

Laser drive current I_LD

Operating current of the laser diode. Allowed: 0 to 20 A.

Laser forward voltage V_f

Voltage across the diode at that current. Allowed: above 0 to 10 V.

Optical output power P_opt

Light that leaves the chip. It does not heat the cold stage, so it is subtracted from the electrical input. Allowed: 0 to 20000 mW.

Temperatures and thermal path

Laser set-point temperature T_set

Temperature the controller holds at the sensor, taken as the TEC cold-side temperature. Allowed: -40 to 100 °C.

Reference temperature (ambient or case) T_amb

Air or cold-plate temperature the heat sink rejects heat to. With a heat-sink resistance of 0 this is the case (TEC hot-side) temperature. Allowed: -40 to 100 °C.

Parasitic thermal resistance, case to cold stage R_par

Heat leaks into the cold stage from the case through leads, gas and the fibre or window. Higher is better. Allowed: above 0 to 100000 K/W.

Heat-sink thermal resistance, case to ambient R_hs

0 holds the case at the reference temperature. Above 0, the case warms by the hot-side heat times this resistance, and the calculator iterates to a consistent case temperature. Allowed: 0 to 50 K/W.

Temperature sensor

Thermistor bias current I_b

Current the controller drives through the temperature sensor. Allowed: 0 to 10000 µA.

Thermistor resistance at the set point R_th

Sensor resistance at the set-point temperature (10 kΩ for a 10 kΩ NTC held at 25 °C). Allowed: 0 to 1000 kΩ.

TEC module (datasheet maximum ratings)

TEC maximum current I_max

From the TEC datasheet. Allowed: above 0 to 50 A.

TEC maximum voltage V_max

From the TEC datasheet, at I_max. Allowed: above 0 to 100 V.

TEC maximum temperature difference ΔT_max

From the TEC datasheet, at zero heat load. Allowed: above 0 to 150 K.

Hot-side temperature for those ratings T_h,ref

Hot-side temperature at which the datasheet states I_max, V_max and ΔT_max (27 °C is about 300 K). Allowed: 200 to 400 K.

Results

Q_c, Total heat the TEC must pump: 0.560W
ΔT, Required ΔT, hot side minus cold side: 20.00K
I, TEC current: 0.387A

Heat load

Laser heat (electrical in minus optical out) Q_LD	0.360	W
Parasitic heat leak into the cold stage Q_parNegative when the case is colder than the set point: heat leaks out of the cold stage.	0.200	W
Thermistor self-heating P_sh	0.100	mW
Total heat the TEC must pump Q_c	0.560	W

TEC operating point

Case (TEC hot-side) temperature T_case	45.00	°C
Required ΔT, hot side minus cold side ΔT	20.00	K
TEC current INegative means reversed current: the TEC heats the laser.	0.387	A
TEC current as a share of I_max	21.5	%
TEC voltage V	0.833	V
TEC electrical power P	0.323	W
Heat rejected at the hot side Q_hHeat the heat sink must carry away.	0.883	W
Coefficient of performance COPShown in cooling mode only.	1.74
Cooling capacity at this ΔT (current up to I_max) Q_c,cap	3.246	W
Heat load as a share of that capacity	17.3	%
Heat-sink iterations	1

TEC model from the ratings

Seebeck coefficient S	12.000	mV/K
Electrical resistance R	1.5333	Ω
Thermal conductance K	35.49	mW/K
Maximum heat pumping (ΔT = 0, I = I_max) Q_maxCompare with the datasheet's Q_max as a check on the ratings you entered.	3.996	W

Method and limits

Heat load: the laser's electrical input minus its optical output, plus the parasitic leak from the case into the cold stage, $(T_{\mathrm{case}}-T_{\mathrm{set}})/R_{\mathrm{par}}$ , plus the sensor's self-heating, $I_{\mathrm b}^2R_{\mathrm{th}}$ .

TEC model: the module's Seebeck coefficient S, resistance R and conductance K are derived from $I_{\max}$ , $V_{\max}$ and $\Delta T_{\max}$ at the rated hot-side temperature. The current is the smaller root of $Q_{\mathrm c}=SIT_{\mathrm c}-\tfrac12 I^2R-K\Delta T$ ; a negative current means the TEC heats.

Heat sink: with $R_{\mathrm{hs}}$ above zero the case temperature is $T_{\mathrm{amb}}+Q_{\mathrm h}R_{\mathrm{hs}}$ , which changes $Q_{\mathrm c}$ and $Q_{\mathrm h}$ , so the calculator iterates until the case temperature changes by less than 1 µK.

Capacity: the most heat the TEC can pump at this $\Delta T$ with the current limited to $I_{\max}$ . Compare the load with this, not with $Q_{\max}$ , which applies only at $\Delta T=0$ .

Disclaimer

This calculator uses the ideal thermoelectric equations with module parameters derived from the maximum ratings you enter, held constant at the rated hot-side temperature. It ignores the temperature dependence of the TEC's properties, contact and spreading resistances other than those entered, radiation, and transient behaviour. Results are estimates for early design. Confirm them against the TEC manufacturer's performance data and by measurement before you commit a design. Provided as is, without warranty.

References

H. Lee, A. M. Attar, S. L. Weera, "Performance prediction of commercial thermoelectric cooler modules using the effective material properties", J. Electronic Materials 44, 2157–2165 (2015), doi:10.1007/s11664-015-3723-7.
Companion application note: "TEC control for laser wavelength stability" (Sample 1).

Equations

Module parameters

\displaystyle S = \frac{V_{\max}}{T_{\mathrm{h,ref}}}

\displaystyle R_{\mathrm{TEC}} = \frac{V_{\max}(T_{\mathrm{h,ref}}-\Delta T_{\max})}{T_{\mathrm{h,ref}}I_{\max}}

\displaystyle K_{\mathrm{TEC}} = \frac{V_{\max}I_{\max}(T_{\mathrm{h,ref}}-\Delta T_{\max})}{2T_{\mathrm{h,ref}}\Delta T_{\max}}

\displaystyle Q_{\max} = \frac{V_{\max}I_{\max}(T_{\mathrm{h,ref}}+\Delta T_{\max})}{2T_{\mathrm{h,ref}}}

Absolute temperatures are in kelvin. Module parameters are held at the rated hot-side temperature.

Cold-side heat load

\displaystyle P_{\mathrm{el}} = I_{\mathrm{LD}}V_{\mathrm f}

\displaystyle Q_{\mathrm{LD}} = P_{\mathrm{el}}-P_{\mathrm{opt}}

\displaystyle P_{\mathrm{sh}} = I_{\mathrm{bias}}^2R_{\mathrm{th}}

\displaystyle Q_{\mathrm{par}} = \frac{T_{\mathrm{case}}-T_{\mathrm{set}}}{R_{\mathrm{par}}}

\displaystyle Q_{\mathrm c} = Q_{\mathrm{LD}}+Q_{\mathrm{par}}+P_{\mathrm{sh}}

Powers, currents and resistances are converted to watts, amperes and ohms before evaluation.

Operating current and hot side

\displaystyle \Delta T = T_{\mathrm h}-T_{\mathrm c}

\displaystyle b = ST_{\mathrm c},\qquad c = Q_{\mathrm c}+K_{\mathrm{TEC}}\Delta T

\displaystyle I_{\mathrm{TEC}} = \frac{b-\sqrt{b^2-2R_{\mathrm{TEC}}c}}{R_{\mathrm{TEC}}}

\displaystyle V_{\mathrm{TEC}} = S\Delta T+I_{\mathrm{TEC}}R_{\mathrm{TEC}}

\displaystyle P_{\mathrm{TEC}} = I_{\mathrm{TEC}}V_{\mathrm{TEC}}

\displaystyle Q_{\mathrm h} = Q_{\mathrm c}+P_{\mathrm{TEC}}

\displaystyle T_{\mathrm{case}}^{\mathrm{next}} = T_{\mathrm{amb}}+Q_{\mathrm h}R_{\mathrm{hs}}

Iterate the case temperature until its change is below 1 µK, up to 200 iterations. The discriminant must be nonnegative and current must stay within the entered rating.

Capacity and efficiency

\displaystyle I_{\mathrm{opt}} = \min\left(\frac{ST_{\mathrm c}}{R_{\mathrm{TEC}}},I_{\max}\right)

\displaystyle Q_{\mathrm{c,cap}} = SI_{\mathrm{opt}}T_{\mathrm c}-\frac{I_{\mathrm{opt}}^2R_{\mathrm{TEC}}}{2}-K_{\mathrm{TEC}}\Delta T

\displaystyle \mathrm{COP} = \frac{Q_{\mathrm c}}{P_{\mathrm{TEC}}}

\displaystyle \text{Load fraction} = \frac{Q_{\mathrm c}}{Q_{\mathrm{c,cap}}}

COP requires positive current and input power; load fraction requires positive capacity. The implementation reports zero otherwise.

Calculation steps and constants

P_el = I_ld * V_f
require  P_opt == 0 or P_opt * W_per_mW < P_el
require  dT_max < Th_ref
S = V_max / Th_ref
R_tec = V_max * (Th_ref - dT_max) / (Th_ref * I_max)
K_tec = V_max * I_max * (Th_ref - dT_max) / (2 * Th_ref * dT_max)
Q_max = V_max * I_max * (Th_ref + dT_max) / (2 * Th_ref)
T_c = T_set + C_to_K
Q_LD = P_el - P_opt * W_per_mW
P_sh = (I_bias * A_per_uA)^2 * (R_th * ohm_per_kohm)
T_case = T_amb
repeat (at most 200 times):
    T_h = T_case + C_to_K
    dT = T_h - T_c
    Q_par = (T_case - T_set) / R_par
    Q_c = Q_LD + Q_par + P_sh
    b_q = S * T_c
    c_q = Q_c + K_tec * dT
    disc = b_q^2 - 2 * R_tec * c_q
    require  disc >= 0
    I_tec = (b_q - sqrt(disc)) / R_tec
    require  abs(I_tec) <= I_max
    V_tec = S * dT + I_tec * R_tec
    P_tec = I_tec * V_tec
    Q_h = Q_c + P_tec
    next T_case = T_amb + Q_h * R_hs
until |next - T_case| < 1e-06 °C
I_frac = I_tec / I_max
COP = if(I_tec > 0 and P_tec > 0, Q_c / P_tec, 0)
I_opt = min(S * T_c / R_tec, I_max)
Qc_cap = S * I_opt * T_c - 0.5 * I_opt^2 * R_tec - K_tec * dT
load_frac = if(Qc_cap > 0, Q_c / Qc_cap, 0)
load_pct = load_frac * pct

constants:
    C_to_K = 273.15 K
    W_per_mW = 0.001 W/mW
    mW_per_W = 1000 mW/W
    mV_per_V = 1000 mV/V
    A_per_uA = 1e-06 A/µA
    ohm_per_kohm = 1000 Ω/kΩ
    pct = 100 %
    load_warn = 0.7
    model_dT_warn = 25 K

Jezdan Gomez · Technical documents and tools for photonics

TEC heat load v1.0.0 · calc engine 1.0.0 · config 8db3b090ad35