I’ve got this little cable here, I don’t know if you can see it.
Show a little coax cable
and if I can overlap, and I took my ohmmeter,
and I
connected between the front, the signal and return on my
on my little 1-foot-long cable, my 30-centimeter cable.
Of course, what would the ohmmeter read?
In the end, of course, is open over here.
What would the ohmmeter read when I connect between the signal return my
my 30-centimeter-long cable? Nothing.
It’d be…
You mean 0? Very high impedance. Very high.
Robert: Resistance. Eric: It being open.
Yeah. It being open, resistance is open, right.
But now I've taken that cable, and I've made it
450,000 kilometers long stretching the earth to the moon.
Takes 3 seconds
for a signal to go down to the end and then come back, right.
So, now what does my ohmmeter read?
Because and the ohmmeter, these ohmmeters are pretty fast these days.
It updates every half a second.
And so, when I connect
my ohmmeter between the
the front of my transmission line,
I could do a reading in half a second.
And every half a second thereafter.
What will my ohmmeter read?
This is one of those really simple concepts,
that really challenge our fundamental understanding intuition.
So, it updates every 0.5 seconds,
and it takes from here to here
is this the moon,
it takes
1 nanos… No, I'm sorry.
Let's see if I can do my eraser here.
It takes,
so it takes
1 second
as the
one-way time delay.
So,
what's my ohmmeter gonna read?
So, I got this really long cable, I'm looking on the front end,
I stick my ohmmeter to this signal return,
what's it gonna read?
When it was really short, it was an open, right.
When it’s really long, what it's gonna be? Well,
when I launch,
when I connect the end of my
ohmmeter to the end of the cable.
I apply a 1-volt signal.
What is that 1-volt signal initially,
what is that instantaneous impedance that I see
as soon as I connect that 1-volt signal
between the signal and return.
Well, I see an impedance of 50 ohms.
And so initially, I'm gonna get, let's see,
a 1 volt individual, I'm gonna get 20 milliamps.
And what is that
20 milliamps of current? What's that
that voltage wavefront, I just increased the voltage here.
What's that voltage signal gonna do?
That 1-volt signal is gonna propagate.
It's gonna zip down this very long transmission line
there, because that that is the second innovation that
Maxwell introduced this idea that
if I have a changing electric field, so I
increased the voltage,
I've increased the electric field in that region
between the signal and the return,
that changing electric field generates a changing magnetic field,
the changing magnetic field generates a change in electric field
and it self-propagates.
So, it’s going to read like 50 ohms?
It is.
I'm gonna get that signal propagating down the transmission line
at the speed of light in the vacuum of the coax cable,
it's gonna propagate at
30 centimeters per nanosecond,
it's gonna zip down that line
and in its wake,
it's gonna leave, there's gonna be a signal going in, a return,
signal,
return, signal,
return,
it’s gonna be the signal propagating down as conduction current.
Wherever I have that changing electric field. I know where you are going with this.
And so, what do I see going in here? I launched a signal
20 milliamps comes in,
20 milliamps comes out,
my voltmeter applies a constant 1 volt,
it reads 20 milliamps going this way, 20 milliamps going this way
and I say oh, the input resistance, because that's all my ohmmeter reads,
the input resistance is
50 ohms.
But wait a minute. It's open over here,
I left it, I pulled that LED and it's open.
How is it possible for me to send,
attach my voltmeter, my ohmmeter,
and measure 50 ohms when it's open to the far end?
And that's because
the input impedance of this transmission line changes.
If I
initially launch, connect my
my ohmmeter and I launch that
1-volt signal down that line,
it takes 1 second to go down,
what's it gonna do when it hits the open?
It's gonna reflect,
and now it's gonna be a 1 volt going this way
and it's gonna be a signal, return, signal, return, signal, return,
it's gonna propagate in the other direction,
it's gonna take another second to come down,
and now let's see this current’s moving this way initially,
the
return current is gonna go the other way,
these two currents are gonna cancel out
and suddenly
as soon as the reflection gets here, and it's at 50 ohms
over here in the
in the source, as soon as it gets here,
those two currents gonna cancel out.
And if I look overtime
and I look at the
input impedance, input resistance,
versus time
I turn on, I'm gonna get 50 ohms, 50 ohms, 50 ohms,
and then one second to go down,
one second to come back, so here's the one second mark,
here's the two second mark,
and then it's gonna be infinite after two seconds.
The input impedance, the cable changes
based on how long it takes for that signal to go down and back.
And now, let's go back to, so here is
between the earth and the moon
450,000 kilometers,
one second one way timed like, two second round trip time.
In those two seconds that I'm doing the measurement,
my very slow digital multimeter, my very slow ohmmeter
is gonna measure the input resistance 50 ohms.
Literally with an ohmmeter.
Because that's how it behaves. It looks like,
it looks like
a resistor at the front end,
because I have a constant voltage applied
and a constant current,
and that is the very definition of a resistor.
If I have an ohmmeter, it's really slow.
That takes half a second to work.
I have to have a
transmission line that's at least one second,
or I'm sorry, at least half a second time delay
in order for me to see the resistance that front end with my slow ohmmeter.
The shorter I make that cable,
the shorter time I have
to measure that constant input
impedance or resistance.
And now I go back to earth’s or lab scale dimensions.
If I have only
a 30 centimeters long
or if I have 1 meter long,
1 meter long that's in air, in air
1 meter long,
that's 3 nanoseconds to go down,
3 nanoseconds to come back
in order to measure that constant input resistance I need an ohmmeter,
that can do a measurement in time short compared to
3 nanoseconds down, 3 inch short compared to 6 nanoseconds.
I need an ohmmeter, that can measure that resistance
in, you know, 1 or 2 nanoseconds.
And you can't use a handheld digital multimeter to do that.
You need a really really fast ohmmeter to do that.
And that's kind of what a TDR does.