Suppose I have a resistance with a zero or very low temperature
coefficient (its value stays constant with temperature variation).

At time zero the temperature is T0=20°C and a constant power P is
applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
temperature rises from T0=20°C to Ts where Ts depends on many factors:
mechanical charateristics of the resistance package and the capacity to
dissipate electric heat with the air. Anyway at steady state an balance
is reached and Ts is reached.

I'm interested in the function of T over time. I suppose it's an
exponential function, but what is the time constant? And what's
important for me: does this time constant depend on resistance value?

On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:

>Suppose I have a resistance with a zero or very low temperature
>coefficient (its value stays constant with temperature variation).
>
>At time zero the temperature is T0=20°C and a constant power P is
>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>mechanical charateristics of the resistance package and the capacity to
>dissipate electric heat with the air. Anyway at steady state an balance
>is reached and Ts is reached.
>
>I'm interested in the function of T over time. I suppose it's an
>exponential function, but what is the time constant? And what's
>important for me: does this time constant depend on resistance value?

The temp curve will be kinda exponential looking, probably a bit
flatter. The cooling mechanisms will be nonlinear, especially
radiation.

Soldered to a PC board, you'll see multiple time constants all
tangled. Heat flow is diffusive and messy.

The shape won't depend much on resistor value, given simlar power
dissipation and physical structure and mounting.

An RTD is neat because it can act like a resistor but measure its own
temperature.

https://www.dropbox.com/sh/8t62cgrkpa3alio/AAAkQ2hzZp-JiIh_nIfgzc3oa?dl=0

On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:

>Suppose I have a resistance with a zero or very low temperature
>coefficient (its value stays constant with temperature variation).
>
>At time zero the temperature is T0=20°C and a constant power P is
>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>mechanical charateristics of the resistance package and the capacity to
>dissipate electric heat with the air. Anyway at steady state an balance
>is reached and Ts is reached.
>
>I'm interested in the function of T over time. I suppose it's an
>exponential function, but what is the time constant? And what's
>important for me: does this time constant depend on resistance value?

It will depend on the thermal capacity (specific heat) of the
materials involved, and the thermal resistance of the structure
to the surrounding environment (linearly dependent on surface area
of the boundary). In electronics RC or RL.

There will be a thermal impedance between the power source and
the environmental boundary that produces different spot temperatures,
dependent on the homogeneity of the material volume.

Practically speaking, the quiescent condition is considered if your
measurement doesn't change by a predetermined amount over three
measurements made at predetermined intervals.

In a bang-bang controller situation, you're only concerned about
deltaT between cycles.

If you know the surface area of the homogenous 'radiator'
boundary, you can ballpark the surface temp rise above
ambient as 1 degree C per milliwat per centimeter^2. +/-10%
in free air.

Your heat source can be no cooler than that.

RL

On Monday, November 14, 2022 at 11:31:09 PM UTC-8, pozz wrote:
> Suppose I have a resistance with a zero or very low temperature
> coefficient (its value stays constant with temperature variation).
>
> At time zero the temperature is T0=20°C and a constant power P is
> applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
> temperature rises from T0=20°C to Ts where Ts depends on many factors:
> mechanical charateristics of the resistance package and the capacity to
> dissipate electric heat with the air. Anyway at steady state an balance
> is reached and Ts is reached.
>
> I'm interested in the function of T over time. I suppose it's an
> exponential function, but what is the time constant? And what's
> important for me: does this time constant depend on resistance value?

The more interesting question (because you've specified that the
temperature coefficient is very low for resistance) is what the two-terminal
model suggests as a circuit perturbation. The resistor, in addition to
having resistance, is a different material from the wiring, so each
terminal of the resistor is a thermocouple, and the circuit will get a
spurious voltage according to the terminals' temperature difference.
There will also be heat DELIVERED to those terminals when DC current
flows to the resistor (heat delivered to one terminal, and removed from the other
terminal, by this unintended reversible heat engine).

The thermocouple effects may be very much influenced by the resistor value,
because different resistor ranges might employ different materials, or different
thermal coupling between the terminals.

A Heat Transfer Textbook 5th

https://ahtt.mit.edu/

On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:

>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>
>>Suppose I have a resistance with a zero or very low temperature
>>coefficient (its value stays constant with temperature variation).
>>
>>At time zero the temperature is T0=20°C and a constant power P is
>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>mechanical charateristics of the resistance package and the capacity to
>>dissipate electric heat with the air. Anyway at steady state an balance
>>is reached and Ts is reached.
>>
>>I'm interested in the function of T over time. I suppose it's an
>>exponential function, but what is the time constant? And what's
>>important for me: does this time constant depend on resistance value?
>
>It will depend on the thermal capacity (specific heat) of the
>materials involved, and the thermal resistance of the structure
>to the surrounding environment (linearly dependent on surface area
>of the boundary). In electronics RC or RL.

Cooling is not linear on surface area. If you heat sink to an infinite
plane, theta is not zero.

>
>There will be a thermal impedance between the power source and
>the environmental boundary that produces different spot temperatures,
>dependent on the homogeneity of the material volume.
>
>Practically speaking, the quiescent condition is considered if your
>measurement doesn't change by a predetermined amount over three
>measurements made at predetermined intervals.
>
>In a bang-bang controller situation, you're only concerned about
>deltaT between cycles.
>
>If you know the surface area of the homogenous 'radiator'
>boundary, you can ballpark the surface temp rise above
>ambient as 1 degree C per milliwat per centimeter^2. +/-10%
>in free air.
>
>Your heat source can be no cooler than that.
>
>RL

On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
<jlarkin@highland_atwork_technology.com> wrote:

>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>
>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>
>>>Suppose I have a resistance with a zero or very low temperature
>>>coefficient (its value stays constant with temperature variation).
>>>
>>>At time zero the temperature is T0=20°C and a constant power P is
>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>mechanical charateristics of the resistance package and the capacity to
>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>is reached and Ts is reached.
>>>
>>>I'm interested in the function of T over time. I suppose it's an
>>>exponential function, but what is the time constant? And what's
>>>important for me: does this time constant depend on resistance value?
>>
>>It will depend on the thermal capacity (specific heat) of the
>>materials involved, and the thermal resistance of the structure
>>to the surrounding environment (linearly dependent on surface area
>>of the boundary). In electronics RC or RL.
>
>Cooling is not linear on surface area. If you heat sink to an infinite
>plane, theta is not zero.
>

It's linear over practical ranges, on avaerage, in a defined
environment.

If there's a range of conditions, you just pick the worst
(and keep it out of direct sunlight, where permitted).

RL

On Tuesday, November 15, 2022 at 4:50:41 PM UTC-8, legg wrote:
> On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
> <jlarkin@highland_atwork_technology.com> wrote:

> >Cooling is not linear on surface area. If you heat sink to an infinite
> >plane, theta is not zero.
> >
> It's linear over practical ranges, on avaerage, in a defined
> environment.
>
But heat flow follows a diffusion equation, a thermal transient
isn't characterized with those 'average' conditions; the
problem is not an easy mathematical one to solve in
a practical time-dependent case.

Automobile cooling, when the car gets parked, loses the pump; overpressure
and coolant storage/return commonly happens, there's a tank to accomodate that.
Turn off the electronic box, and the fan stops?

On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:

>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
><jlarkin@highland_atwork_technology.com> wrote:
>
>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>
>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>
>>>>Suppose I have a resistance with a zero or very low temperature
>>>>coefficient (its value stays constant with temperature variation).
>>>>
>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>mechanical charateristics of the resistance package and the capacity to
>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>is reached and Ts is reached.
>>>>
>>>>I'm interested in the function of T over time. I suppose it's an
>>>>exponential function, but what is the time constant? And what's
>>>>important for me: does this time constant depend on resistance value?
>>>
>>>It will depend on the thermal capacity (specific heat) of the
>>>materials involved, and the thermal resistance of the structure
>>>to the surrounding environment (linearly dependent on surface area
>>>of the boundary). In electronics RC or RL.
>>
>>Cooling is not linear on surface area. If you heat sink to an infinite
>>plane, theta is not zero.
>>
>
>It's linear over practical ranges, on avaerage, in a defined
>environment.
>
>If there's a range of conditions, you just pick the worst
>(and keep it out of direct sunlight, where permitted).
>
>RL

It's common to make a chassis out of 0.062" thick aluminum. And not
unusual to heat sink a TO-220 transistor to that chassis.

So, what is theta of a TO-220 transistor bolted to such a chassis?
Assume no insulator and an infinitely large chassis.

How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?

Spreading thermal resistance soon makes a bigger sheet stop doing any
good.

On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
<jlarkin@highlandSNIPMEtechnology.com> wrote:

>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>
>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>><jlarkin@highland_atwork_technology.com> wrote:
>>
>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>
>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>
>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>coefficient (its value stays constant with temperature variation).
>>>>>
>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>is reached and Ts is reached.
>>>>>
>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>exponential function, but what is the time constant? And what's
>>>>>important for me: does this time constant depend on resistance value?
>>>>
>>>>It will depend on the thermal capacity (specific heat) of the
>>>>materials involved, and the thermal resistance of the structure
>>>>to the surrounding environment (linearly dependent on surface area
>>>>of the boundary). In electronics RC or RL.
>>>
>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>plane, theta is not zero.
>>>
>>
>>It's linear over practical ranges, on avaerage, in a defined
>>environment.
>>
>>If there's a range of conditions, you just pick the worst
>>(and keep it out of direct sunlight, where permitted).
>>
>>RL
>
>It's common to make a chassis out of 0.062" thick aluminum. And not
>unusual to heat sink a TO-220 transistor to that chassis.
>
>So, what is theta of a TO-220 transistor bolted to such a chassis?
>Assume no insulator and an infinitely large chassis.
>
>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>
>Spreading thermal resistance soon makes a bigger sheet stop doing any
>good.

I'm talking boxes, not sheets.

I treat a U channel or flat plate as 2 dimensuional surfaces
and use the standard surface rise equation, to get the average.
There will be a delta T across the plate. At each spot point,
the surface temperature will tell you how much power is being
dissipated (per sq cm) from that location.

Fiddle with thickness, surface finish, color; its all the same.
Force airflow, and it's a different story.

RL

On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:

>Suppose I have a resistance with a zero or very low temperature
>coefficient (its value stays constant with temperature variation).
>
>At time zero the temperature is T0=20°C and a constant power P is
>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>mechanical charateristics of the resistance package and the capacity to
>dissipate electric heat with the air. Anyway at steady state an balance
>is reached and Ts is reached.
>
>I'm interested in the function of T over time. I suppose it's an
>exponential function, but what is the time constant? And what's
>important for me: does this time constant depend on resistance value?

The temperature rise of the heat source, your 'resistor' is determined
by the thermal impedance to ambient.

As the physical size of the source reduces, it's thermal impedance to
the surrounding dissipator rises. Early thermal modeling programs
with point of source power elements showed ridiculous values at that
one spot. Make it small enough and it'll approach the temperature
of a star, without any effect on the surrounding larger area
of conductively dissipative media.

RL

On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:

>On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
><jlarkin@highlandSNIPMEtechnology.com> wrote:
>
>>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>
>>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>><jlarkin@highland_atwork_technology.com> wrote:
>>>
>>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>
>>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>
>>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>>coefficient (its value stays constant with temperature variation).
>>>>>>
>>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>is reached and Ts is reached.
>>>>>>
>>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>>exponential function, but what is the time constant? And what's
>>>>>>important for me: does this time constant depend on resistance value?
>>>>>
>>>>>It will depend on the thermal capacity (specific heat) of the
>>>>>materials involved, and the thermal resistance of the structure
>>>>>to the surrounding environment (linearly dependent on surface area
>>>>>of the boundary). In electronics RC or RL.
>>>>
>>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>>plane, theta is not zero.
>>>>
>>>
>>>It's linear over practical ranges, on avaerage, in a defined
>>>environment.
>>>
>>>If there's a range of conditions, you just pick the worst
>>>(and keep it out of direct sunlight, where permitted).
>>>
>>>RL
>>
>>It's common to make a chassis out of 0.062" thick aluminum. And not
>>unusual to heat sink a TO-220 transistor to that chassis.
>>
>>So, what is theta of a TO-220 transistor bolted to such a chassis?
>>Assume no insulator and an infinitely large chassis.
>>
>>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>
>>Spreading thermal resistance soon makes a bigger sheet stop doing any
>>good.
>
>I'm talking boxes, not sheets.

The top or bottom or side of a box is a sheet. If it's infinitely big,
the transistor can't know if it's a box or a sheet.

So what's theta?

>
>I treat a U channel or flat plate as 2 dimensuional surfaces
>and use the standard surface rise equation, to get the average.
>There will be a delta T across the plate. At each spot point,
>the surface temperature will tell you how much power is being
>dissipated (per sq cm) from that location.

Sure. How many K/W? Theory is fun, until the transistor fails.

On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
<jlarkin@highland_atwork_technology.com> wrote:

>On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>
>>On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>><jlarkin@highlandSNIPMEtechnology.com> wrote:
>>
>>>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>
>>>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>><jlarkin@highland_atwork_technology.com> wrote:
>>>>
>>>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>
>>>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>
>>>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>>>coefficient (its value stays constant with temperature variation).
>>>>>>>
>>>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>is reached and Ts is reached.
>>>>>>>
>>>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>>>exponential function, but what is the time constant? And what's
>>>>>>>important for me: does this time constant depend on resistance value?
>>>>>>
>>>>>>It will depend on the thermal capacity (specific heat) of the
>>>>>>materials involved, and the thermal resistance of the structure
>>>>>>to the surrounding environment (linearly dependent on surface area
>>>>>>of the boundary). In electronics RC or RL.
>>>>>
>>>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>plane, theta is not zero.
>>>>>
>>>>
>>>>It's linear over practical ranges, on avaerage, in a defined
>>>>environment.
>>>>
>>>>If there's a range of conditions, you just pick the worst
>>>>(and keep it out of direct sunlight, where permitted).
>>>>
>>>>RL
>>>
>>>It's common to make a chassis out of 0.062" thick aluminum. And not
>>>unusual to heat sink a TO-220 transistor to that chassis.
>>>
>>>So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>Assume no insulator and an infinitely large chassis.
>>>
>>>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>
>>>Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>good.
>>
>>I'm talking boxes, not sheets.
>
>The top or bottom or side of a box is a sheet. If it's infinitely big,
>the transistor can't know if it's a box or a sheet.
>
>So what's theta?
>
>>
>>I treat a U channel or flat plate as 2 dimensuional surfaces
>>and use the standard surface rise equation, to get the average.
>>There will be a delta T across the plate. At each spot point,
>>the surface temperature will tell you how much power is being
>>dissipated (per sq cm) from that location.
>
>Sure. How many K/W? Theory is fun, until the transistor fails.

Infinite is theory, mw per cm^2 surface area is reality.

The aim is to reduce the thermal impedance to the practical
physical boundary of, in most cases, the external ambient
environment.

RL

On Thu, 17 Nov 2022 11:07:18 -0500, legg <legg@nospam.magma.ca> wrote:

>On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
><jlarkin@highland_atwork_technology.com> wrote:
>
>>On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>>
>>>On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>>><jlarkin@highlandSNIPMEtechnology.com> wrote:
>>>
>>>>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>
>>>>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>>><jlarkin@highland_atwork_technology.com> wrote:
>>>>>
>>>>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>
>>>>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>>
>>>>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>>>>coefficient (its value stays constant with temperature variation).
>>>>>>>>
>>>>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>>is reached and Ts is reached.
>>>>>>>>
>>>>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>>>>exponential function, but what is the time constant? And what's
>>>>>>>>important for me: does this time constant depend on resistance value?
>>>>>>>
>>>>>>>It will depend on the thermal capacity (specific heat) of the
>>>>>>>materials involved, and the thermal resistance of the structure
>>>>>>>to the surrounding environment (linearly dependent on surface area
>>>>>>>of the boundary). In electronics RC or RL.
>>>>>>
>>>>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>>plane, theta is not zero.
>>>>>>
>>>>>
>>>>>It's linear over practical ranges, on avaerage, in a defined
>>>>>environment.
>>>>>
>>>>>If there's a range of conditions, you just pick the worst
>>>>>(and keep it out of direct sunlight, where permitted).
>>>>>
>>>>>RL
>>>>
>>>>It's common to make a chassis out of 0.062" thick aluminum. And not
>>>>unusual to heat sink a TO-220 transistor to that chassis.
>>>>
>>>>So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>>Assume no insulator and an infinitely large chassis.
>>>>
>>>>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>>
>>>>Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>>good.
>>>
>>>I'm talking boxes, not sheets.
>>
>>The top or bottom or side of a box is a sheet. If it's infinitely big,
>>the transistor can't know if it's a box or a sheet.
>>
>>So what's theta?
>>
>>>
>>>I treat a U channel or flat plate as 2 dimensuional surfaces
>>>and use the standard surface rise equation, to get the average.
>>>There will be a delta T across the plate. At each spot point,
>>>the surface temperature will tell you how much power is being
>>>dissipated (per sq cm) from that location.
>>
>>Sure. How many K/W? Theory is fun, until the transistor fails.
>
>Infinite is theory, mw per cm^2 surface area is reality.
>
>The aim is to reduce the thermal impedance to the practical
>physical boundary of, in most cases, the external ambient
>environment.
>
>RL

So: given an infinite sheet of 0.062 thick aluminum, and a TO-220
bolted to it, what's the transistor theta?

And how big a sheet is close enough to infinite as makes no practical
difference?

That is a very real situation and deserves real numbers.

Any guesses?

And a bonus question, how would theta change if we used a TO-247?

On Thu, 17 Nov 2022 12:53:43 -0800, John Larkin
<jlarkin@highlandSNIPMEtechnology.com> wrote:

>On Thu, 17 Nov 2022 11:07:18 -0500, legg <legg@nospam.magma.ca> wrote:
>
>>On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
>><jlarkin@highland_atwork_technology.com> wrote:
>>
>>>On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>>>
>>>>On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>>>><jlarkin@highlandSNIPMEtechnology.com> wrote:
>>>>
>>>>>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>
>>>>>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>>>><jlarkin@highland_atwork_technology.com> wrote:
>>>>>>
>>>>>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>>
>>>>>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>>>
>>>>>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>>>>>coefficient (its value stays constant with temperature variation).
>>>>>>>>>
>>>>>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>>>is reached and Ts is reached.
>>>>>>>>>
>>>>>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>>>>>exponential function, but what is the time constant? And what's
>>>>>>>>>important for me: does this time constant depend on resistance value?
>>>>>>>>
>>>>>>>>It will depend on the thermal capacity (specific heat) of the
>>>>>>>>materials involved, and the thermal resistance of the structure
>>>>>>>>to the surrounding environment (linearly dependent on surface area
>>>>>>>>of the boundary). In electronics RC or RL.
>>>>>>>
>>>>>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>>>plane, theta is not zero.
>>>>>>>
>>>>>>
>>>>>>It's linear over practical ranges, on avaerage, in a defined
>>>>>>environment.
>>>>>>
>>>>>>If there's a range of conditions, you just pick the worst
>>>>>>(and keep it out of direct sunlight, where permitted).
>>>>>>
>>>>>>RL
>>>>>
>>>>>It's common to make a chassis out of 0.062" thick aluminum. And not
>>>>>unusual to heat sink a TO-220 transistor to that chassis.
>>>>>
>>>>>So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>>>Assume no insulator and an infinitely large chassis.
>>>>>
>>>>>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>>>
>>>>>Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>>>good.
>>>>
>>>>I'm talking boxes, not sheets.
>>>
>>>The top or bottom or side of a box is a sheet. If it's infinitely big,
>>>the transistor can't know if it's a box or a sheet.
>>>
>>>So what's theta?
>>>
>>>>
>>>>I treat a U channel or flat plate as 2 dimensuional surfaces
>>>>and use the standard surface rise equation, to get the average.
>>>>There will be a delta T across the plate. At each spot point,
>>>>the surface temperature will tell you how much power is being
>>>>dissipated (per sq cm) from that location.
>>>
>>>Sure. How many K/W? Theory is fun, until the transistor fails.
>>
>>Infinite is theory, mw per cm^2 surface area is reality.
>>
>>The aim is to reduce the thermal impedance to the practical
>>physical boundary of, in most cases, the external ambient
>>environment.
>>
>>RL
>
>So: given an infinite sheet of 0.062 thick aluminum, and a TO-220
>bolted to it, what's the transistor theta?
>
>And how big a sheet is close enough to infinite as makes no practical
>difference?
>
>That is a very real situation and deserves real numbers.
>
>Any guesses?
>
>And a bonus question, how would theta change if we used a TO-247?

Infinity, by definition, is an unreal number.

I used to limit my calculations to hardware between matchbox
and breadbox sizes - and have demonstrated them in physical
hatrdware in more than a few instances when pointy heads
wanted a chair and computer station occupied to 'solve the
problem'.

I was surprised to see that iwas also true in a multi-moduled,
multi-physical media hardware with vibrating surfaces that had
basic conglomertates measuring 1.5' x 2' x4', and that also
required stacking of units. Thankfully, I managed to avoid
solar insolation.

That was a bitch to demonstrate, with thermocouples built-in
and requiring many long-term (some hours) iterations with
different power levels and stacking arangements.

After each of these past physical demonstrations, I had no
further arguments, and the pointy heads went off to address
other things that they didn't understand, elsewhere.

So, get real.

RL

On Thu, 17 Nov 2022 18:09:48 -0500, legg <legg@nospam.magma.ca> wrote:

>On Thu, 17 Nov 2022 12:53:43 -0800, John Larkin
><jlarkin@highlandSNIPMEtechnology.com> wrote:
>
>>On Thu, 17 Nov 2022 11:07:18 -0500, legg <legg@nospam.magma.ca> wrote:
>>
>>>On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
>>><jlarkin@highland_atwork_technology.com> wrote:
>>>
>>>>On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>
>>>>>On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>>>>><jlarkin@highlandSNIPMEtechnology.com> wrote:
>>>>>
>>>>>>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>
>>>>>>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>>>>><jlarkin@highland_atwork_technology.com> wrote:
>>>>>>>
>>>>>>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>>>
>>>>>>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>>>>
>>>>>>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>>>>>>coefficient (its value stays constant with temperature variation).
>>>>>>>>>>
>>>>>>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>>>>is reached and Ts is reached.
>>>>>>>>>>
>>>>>>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>>>>>>exponential function, but what is the time constant? And what's
>>>>>>>>>>important for me: does this time constant depend on resistance value?
>>>>>>>>>
>>>>>>>>>It will depend on the thermal capacity (specific heat) of the
>>>>>>>>>materials involved, and the thermal resistance of the structure
>>>>>>>>>to the surrounding environment (linearly dependent on surface area
>>>>>>>>>of the boundary). In electronics RC or RL.
>>>>>>>>
>>>>>>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>>>>plane, theta is not zero.
>>>>>>>>
>>>>>>>
>>>>>>>It's linear over practical ranges, on avaerage, in a defined
>>>>>>>environment.
>>>>>>>
>>>>>>>If there's a range of conditions, you just pick the worst
>>>>>>>(and keep it out of direct sunlight, where permitted).
>>>>>>>
>>>>>>>RL
>>>>>>
>>>>>>It's common to make a chassis out of 0.062" thick aluminum. And not
>>>>>>unusual to heat sink a TO-220 transistor to that chassis.
>>>>>>
>>>>>>So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>>>>Assume no insulator and an infinitely large chassis.
>>>>>>
>>>>>>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>>>>
>>>>>>Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>>>>good.
>>>>>
>>>>>I'm talking boxes, not sheets.
>>>>
>>>>The top or bottom or side of a box is a sheet. If it's infinitely big,
>>>>the transistor can't know if it's a box or a sheet.
>>>>
>>>>So what's theta?
>>>>
>>>>>
>>>>>I treat a U channel or flat plate as 2 dimensuional surfaces
>>>>>and use the standard surface rise equation, to get the average.
>>>>>There will be a delta T across the plate. At each spot point,
>>>>>the surface temperature will tell you how much power is being
>>>>>dissipated (per sq cm) from that location.
>>>>
>>>>Sure. How many K/W? Theory is fun, until the transistor fails.
>>>
>>>Infinite is theory, mw per cm^2 surface area is reality.
>>>
>>>The aim is to reduce the thermal impedance to the practical
>>>physical boundary of, in most cases, the external ambient
>>>environment.
>>>
>>>RL
>>
>>So: given an infinite sheet of 0.062 thick aluminum, and a TO-220
>>bolted to it, what's the transistor theta?
>>
>>And how big a sheet is close enough to infinite as makes no practical
>>difference?
>>
>>That is a very real situation and deserves real numbers.
>>
>>Any guesses?
>>
>>And a bonus question, how would theta change if we used a TO-247?
>
>Infinity, by definition, is an unreal number.

You won't accept the concept of an infinite sheet? It's useful here.

>
>I used to limit my calculations to hardware between matchbox
>and breadbox sizes - and have demonstrated them in physical
>hatrdware in more than a few instances when pointy heads
>wanted a chair and computer station occupied to 'solve the
>problem'.
>
>I was surprised to see that iwas also true in a multi-moduled,
>multi-physical media hardware with vibrating surfaces that had
>basic conglomertates measuring 1.5' x 2' x4', and that also
>required stacking of units. Thankfully, I managed to avoid
>solar insolation.
>
>That was a bitch to demonstrate, with thermocouples built-in
>and requiring many long-term (some hours) iterations with
>different power levels and stacking arangements.
>
>After each of these past physical demonstrations, I had no
>further arguments, and the pointy heads went off to address
>other things that they didn't understand, elsewhere.
>
>So, get real.
>
>RL

No numbers. No guesses. OK.

On 17/11/2022 20:53, John Larkin wrote:
> On Thu, 17 Nov 2022 11:07:18 -0500, legg <legg@nospam.magma.ca> wrote:
>
>> On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
>> <jlarkin@highland_atwork_technology.com> wrote:
>>
>>> On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>>>
>>>> On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>>>> <jlarkin@highlandSNIPMEtechnology.com> wrote:
>>>>
>>>>> On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>
>>>>>> On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>>>> <jlarkin@highland_atwork_technology.com> wrote:
>>>>>>
>>>>>>> On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>>
>>>>>>>> On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>>>
>>>>>>>>> Suppose I have a resistance with a zero or very low temperature
>>>>>>>>> coefficient (its value stays constant with temperature variation).
>>>>>>>>>
>>>>>>>>> At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>>> applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>>> temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>>> mechanical charateristics of the resistance package and the capacity to
>>>>>>>>> dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>>> is reached and Ts is reached.
>>>>>>>>>
>>>>>>>>> I'm interested in the function of T over time. I suppose it's an
>>>>>>>>> exponential function, but what is the time constant? And what's
>>>>>>>>> important for me: does this time constant depend on resistance value?
>>>>>>>>
>>>>>>>> It will depend on the thermal capacity (specific heat) of the
>>>>>>>> materials involved, and the thermal resistance of the structure
>>>>>>>> to the surrounding environment (linearly dependent on surface area
>>>>>>>> of the boundary). In electronics RC or RL.
>>>>>>>
>>>>>>> Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>>> plane, theta is not zero.
>>>>>>>
>>>>>>
>>>>>> It's linear over practical ranges, on avaerage, in a defined
>>>>>> environment.
>>>>>>
>>>>>> If there's a range of conditions, you just pick the worst
>>>>>> (and keep it out of direct sunlight, where permitted).
>>>>>>
>>>>>> RL
>>>>>
>>>>> It's common to make a chassis out of 0.062" thick aluminum. And not
>>>>> unusual to heat sink a TO-220 transistor to that chassis.
>>>>>
>>>>> So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>>> Assume no insulator and an infinitely large chassis.
>>>>>
>>>>> How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>>>
>>>>> Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>>> good.
>>>>
>>>> I'm talking boxes, not sheets.
>>>
>>> The top or bottom or side of a box is a sheet. If it's infinitely big,
>>> the transistor can't know if it's a box or a sheet.
>>>
>>> So what's theta?
>>>
>>>>
>>>> I treat a U channel or flat plate as 2 dimensuional surfaces
>>>> and use the standard surface rise equation, to get the average.
>>>> There will be a delta T across the plate. At each spot point,
>>>> the surface temperature will tell you how much power is being
>>>> dissipated (per sq cm) from that location.
>>>
>>> Sure. How many K/W? Theory is fun, until the transistor fails.
>>
>> Infinite is theory, mw per cm^2 surface area is reality.
>>
>> The aim is to reduce the thermal impedance to the practical
>> physical boundary of, in most cases, the external ambient
>> environment.
>>
>> RL
>
> So: given an infinite sheet of 0.062 thick aluminum, and a TO-220
> bolted to it, what's the transistor theta?
>
> And how big a sheet is close enough to infinite as makes no practical
> difference?
>
> That is a very real situation and deserves real numbers.
>
> Any guesses?
>
> And a bonus question, how would theta change if we used a TO-247?
>

You want guesses, I give you guesses. TO-220 about 1K/W (could be 0.8
could be 1.5)? TO-247 a wee bit lower, say 0.6 to 1.1 K/W ?

piglet

On Thu, 17 Nov 2022 16:36:23 -0800, John Larkin
<jlarkin@highlandSNIPMEtechnology.com> wrote:

>On Thu, 17 Nov 2022 18:09:48 -0500, legg <legg@nospam.magma.ca> wrote:
>
>>On Thu, 17 Nov 2022 12:53:43 -0800, John Larkin
>><jlarkin@highlandSNIPMEtechnology.com> wrote:
>>
>>>On Thu, 17 Nov 2022 11:07:18 -0500, legg <legg@nospam.magma.ca> wrote:
>>>
>>>>On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
>>>><jlarkin@highland_atwork_technology.com> wrote:
>>>>
>>>>>On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>
>>>>>>On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>>>>>><jlarkin@highlandSNIPMEtechnology.com> wrote:
>>>>>>
>>>>>>>On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>>
>>>>>>>>On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>>>>>><jlarkin@highland_atwork_technology.com> wrote:
>>>>>>>>
>>>>>>>>>On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>>>>
>>>>>>>>>>On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>>>>>
>>>>>>>>>>>Suppose I have a resistance with a zero or very low temperature
>>>>>>>>>>>coefficient (its value stays constant with temperature variation).
>>>>>>>>>>>
>>>>>>>>>>>At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>>>>>applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>>>>>temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>>>>>mechanical charateristics of the resistance package and the capacity to
>>>>>>>>>>>dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>>>>>is reached and Ts is reached.
>>>>>>>>>>>
>>>>>>>>>>>I'm interested in the function of T over time. I suppose it's an
>>>>>>>>>>>exponential function, but what is the time constant? And what's
>>>>>>>>>>>important for me: does this time constant depend on resistance value?
>>>>>>>>>>
>>>>>>>>>>It will depend on the thermal capacity (specific heat) of the
>>>>>>>>>>materials involved, and the thermal resistance of the structure
>>>>>>>>>>to the surrounding environment (linearly dependent on surface area
>>>>>>>>>>of the boundary). In electronics RC or RL.
>>>>>>>>>
>>>>>>>>>Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>>>>>plane, theta is not zero.
>>>>>>>>>
>>>>>>>>
>>>>>>>>It's linear over practical ranges, on avaerage, in a defined
>>>>>>>>environment.
>>>>>>>>
>>>>>>>>If there's a range of conditions, you just pick the worst
>>>>>>>>(and keep it out of direct sunlight, where permitted).
>>>>>>>>
>>>>>>>>RL
>>>>>>>
>>>>>>>It's common to make a chassis out of 0.062" thick aluminum. And not
>>>>>>>unusual to heat sink a TO-220 transistor to that chassis.
>>>>>>>
>>>>>>>So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>>>>>Assume no insulator and an infinitely large chassis.
>>>>>>>
>>>>>>>How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>>>>>
>>>>>>>Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>>>>>good.
>>>>>>
>>>>>>I'm talking boxes, not sheets.
>>>>>
>>>>>The top or bottom or side of a box is a sheet. If it's infinitely big,
>>>>>the transistor can't know if it's a box or a sheet.
>>>>>
>>>>>So what's theta?
>>>>>
>>>>>>
>>>>>>I treat a U channel or flat plate as 2 dimensuional surfaces
>>>>>>and use the standard surface rise equation, to get the average.
>>>>>>There will be a delta T across the plate. At each spot point,
>>>>>>the surface temperature will tell you how much power is being
>>>>>>dissipated (per sq cm) from that location.
>>>>>
>>>>>Sure. How many K/W? Theory is fun, until the transistor fails.
>>>>
>>>>Infinite is theory, mw per cm^2 surface area is reality.
>>>>
>>>>The aim is to reduce the thermal impedance to the practical
>>>>physical boundary of, in most cases, the external ambient
>>>>environment.
>>>>
>>>>RL
>>>
>>>So: given an infinite sheet of 0.062 thick aluminum, and a TO-220
>>>bolted to it, what's the transistor theta?
>>>
>>>And how big a sheet is close enough to infinite as makes no practical
>>>difference?
>>>
>>>That is a very real situation and deserves real numbers.
>>>
>>>Any guesses?
>>>
>>>And a bonus question, how would theta change if we used a TO-247?
>>
>>Infinity, by definition, is an unreal number.
>
>You won't accept the concept of an infinite sheet? It's useful here.
>
>>
>>I used to limit my calculations to hardware between matchbox
>>and breadbox sizes - and have demonstrated them in physical
>>hatrdware in more than a few instances when pointy heads
>>wanted a chair and computer station occupied to 'solve the
>>problem'.
>>
>>I was surprised to see that iwas also true in a multi-moduled,
>>multi-physical media hardware with vibrating surfaces that had
>>basic conglomertates measuring 1.5' x 2' x4', and that also
>>required stacking of units. Thankfully, I managed to avoid
>>solar insolation.
>>
>>That was a bitch to demonstrate, with thermocouples built-in
>>and requiring many long-term (some hours) iterations with
>>different power levels and stacking arangements.
>>
>>After each of these past physical demonstrations, I had no
>>further arguments, and the pointy heads went off to address
>>other things that they didn't understand, elsewhere.
>>
>>So, get real.
>>
>>RL
>
>No numbers. No guesses. OK.

If the OP wants thermal impedance from his resistor to
ambient, any ambient, he'd need to describe a physical
interface, with dimensions.

If he wanted a thermal time constant, he'd need the volume
and specific heat of the conductive media, and it's surface
area contacting an ambient environment.

Infinite heatsinks don't change Rthjc of a semiconductor,
just the temperature of it's mounting base.

RL

On Fri, 18 Nov 2022 08:44:57 +0000, piglet <erichpwagner@hotmail.com>
wrote:

>On 17/11/2022 20:53, John Larkin wrote:
>> On Thu, 17 Nov 2022 11:07:18 -0500, legg <legg@nospam.magma.ca> wrote:
>>
>>> On Wed, 16 Nov 2022 10:58:16 -0800, John Larkin
>>> <jlarkin@highland_atwork_technology.com> wrote:
>>>
>>>> On Wed, 16 Nov 2022 10:16:40 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>
>>>>> On Tue, 15 Nov 2022 19:30:32 -0800, John Larkin
>>>>> <jlarkin@highlandSNIPMEtechnology.com> wrote:
>>>>>
>>>>>> On Tue, 15 Nov 2022 19:51:43 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>
>>>>>>> On Tue, 15 Nov 2022 16:34:21 -0800, John Larkin
>>>>>>> <jlarkin@highland_atwork_technology.com> wrote:
>>>>>>>
>>>>>>>> On Tue, 15 Nov 2022 08:18:23 -0500, legg <legg@nospam.magma.ca> wrote:
>>>>>>>>
>>>>>>>>> On Tue, 15 Nov 2022 08:31:01 +0100, pozz <pozzugno@gmail.com> wrote:
>>>>>>>>>
>>>>>>>>>> Suppose I have a resistance with a zero or very low temperature
>>>>>>>>>> coefficient (its value stays constant with temperature variation).
>>>>>>>>>>
>>>>>>>>>> At time zero the temperature is T0=20°C and a constant power P is
>>>>>>>>>> applied (i.e. a voltage V=sqrt(P*R)). We know that at steady state the
>>>>>>>>>> temperature rises from T0=20°C to Ts where Ts depends on many factors:
>>>>>>>>>> mechanical charateristics of the resistance package and the capacity to
>>>>>>>>>> dissipate electric heat with the air. Anyway at steady state an balance
>>>>>>>>>> is reached and Ts is reached.
>>>>>>>>>>
>>>>>>>>>> I'm interested in the function of T over time. I suppose it's an
>>>>>>>>>> exponential function, but what is the time constant? And what's
>>>>>>>>>> important for me: does this time constant depend on resistance value?
>>>>>>>>>
>>>>>>>>> It will depend on the thermal capacity (specific heat) of the
>>>>>>>>> materials involved, and the thermal resistance of the structure
>>>>>>>>> to the surrounding environment (linearly dependent on surface area
>>>>>>>>> of the boundary). In electronics RC or RL.
>>>>>>>>
>>>>>>>> Cooling is not linear on surface area. If you heat sink to an infinite
>>>>>>>> plane, theta is not zero.
>>>>>>>>
>>>>>>>
>>>>>>> It's linear over practical ranges, on avaerage, in a defined
>>>>>>> environment.
>>>>>>>
>>>>>>> If there's a range of conditions, you just pick the worst
>>>>>>> (and keep it out of direct sunlight, where permitted).
>>>>>>>
>>>>>>> RL
>>>>>>
>>>>>> It's common to make a chassis out of 0.062" thick aluminum. And not
>>>>>> unusual to heat sink a TO-220 transistor to that chassis.
>>>>>>
>>>>>> So, what is theta of a TO-220 transistor bolted to such a chassis?
>>>>>> Assume no insulator and an infinitely large chassis.
>>>>>>
>>>>>> How about a SOT-89 soldered to an infinitely large 1 oz PCB plane?
>>>>>>
>>>>>> Spreading thermal resistance soon makes a bigger sheet stop doing any
>>>>>> good.
>>>>>
>>>>> I'm talking boxes, not sheets.
>>>>
>>>> The top or bottom or side of a box is a sheet. If it's infinitely big,
>>>> the transistor can't know if it's a box or a sheet.
>>>>
>>>> So what's theta?
>>>>
>>>>>
>>>>> I treat a U channel or flat plate as 2 dimensuional surfaces
>>>>> and use the standard surface rise equation, to get the average.
>>>>> There will be a delta T across the plate. At each spot point,
>>>>> the surface temperature will tell you how much power is being
>>>>> dissipated (per sq cm) from that location.
>>>>
>>>> Sure. How many K/W? Theory is fun, until the transistor fails.
>>>
>>> Infinite is theory, mw per cm^2 surface area is reality.
>>>
>>> The aim is to reduce the thermal impedance to the practical
>>> physical boundary of, in most cases, the external ambient
>>> environment.
>>>
>>> RL
>>
>> So: given an infinite sheet of 0.062 thick aluminum, and a TO-220
>> bolted to it, what's the transistor theta?
>>
>> And how big a sheet is close enough to infinite as makes no practical
>> difference?
>>
>> That is a very real situation and deserves real numbers.
>>
>> Any guesses?
>>
>> And a bonus question, how would theta change if we used a TO-247?
>>
>
>You want guesses, I give you guesses. TO-220 about 1K/W (could be 0.8
>could be 1.5)? TO-247 a wee bit lower, say 0.6 to 1.1 K/W ?
>
>piglet

That's ballpark. I measured 2.3 K/w for a TO220 on a big sheet of .062
aluminum. The sheet was big enough that its edges were close to room
temp, so making it any bigger wouldn't have mattered much. Might get
down to 2.

A TO247 has a contact perimeter that's only about 25% greater, so
theta would drop by about that amount. On a thin sheet, the 247 is no
great advantage.

This sub-thread spun off a statement that a thermal tau would be
linear on some surface area. Usually it's not.

Thermal systems are sufficiently hard to predict that I usually just
build a model and test it. When air flow is involved, analytics are
even harder. We just designed a baffle to distribute air flow from two
fans evenly among 8 PCBs. Envision lots of cardboard and plastic and
tape.