Impedance matching of transmission line to source impedance

[goodphy]

Hello

I'm now studying transmission line theory. I got to know how impedance matching between characteristic impedance of transmission line and electrical load is important to achieve maximum power transfer and minimize power reflection which causes danger for the system.

But the textbook doesn't tell one thing: Impedance matching between source impedance and the line impedance. Is this also important as much as impedance matching between the line and the load?

And also I had some experiment to see impedance matching effect by myself. Our delay generator (DG535, Standford Research) generates TTL signal and output channel impedance can vary between 50 Ohm and High Z. Our lab only has BNC cable of 50 ohm of its characteristic impedance. In experiment, I connected such BNC cable to DG535 and Oscilloscope (OSC). DG535 is set to get source impedance of High Z. When I set OSC impedance of 50 Ohm, I remembered signal was distorted or reduced in amplitude while High Z set gave clean shot.

This is what I really don't understand. The cable and OSC impedance is not matched (50 Ohm, High Z) and why I can get clean signal? It seems contradiction of what I've learned in textbook!

And even source impedance and the cable is also not matched (High Z, 50 Ohm). It is like I have double unmatched points.

Could you tell me how signal can be clean in this case?

 

[EM_Guy]

Let me see if I have this straight:

Characteristic impedance of cable: 50 ohms
Load impedance (OSC): High Z
Source impedance: High Z

In this case, the input impedance (looking into the cable towards the load (OSC)) would be

$Zin = \frac{-jZ0}{tan \beta l}$

Depending on your electrical length from the load, this can be a very high impedance or a very low impedance. If it is a high impedance, then your source impedance and your input impedance looking into the cable are close to matched.

On the other hand, if your source impedance is set to 50 ohms, and your load impedance is high, and if the electrical length of the line is such that the input impedance looking into the line is high, then your source impedance is not matched to your input impedance.

I would advise setting your load impedance and your source impedance to 50 ohms. That way, your input impedance looking into the line should be 50 ohms, and if your source impedance is 50 ohms, you should have a good match.

 

[goodphy]

Let me see if I have this straight:

Characteristic impedance of cable: 50 ohms
Load impedance (OSC): High Z
Source impedance: High Z

In this case, the input impedance (looking into the cable towards the load (OSC)) would be

$Zin = \frac{-jZ0}{tan \beta l}$

Depending on your electrical length from the load, this can be a very high impedance or a very low impedance. If it is a high impedance, then your source impedance and your input impedance looking into the cable are close to matched.

On the other hand, if your source impedance is set to 50 ohms, and your load impedance is high, and if the electrical length of the line is such that the input impedance looking into the line is high, then your source impedance is not matched to your input impedance.

I would advise setting your load impedance and your source impedance to 50 ohms. That way, your input impedance looking into the line should be 50 ohms, and if your source impedance is 50 ohms, you should have a good match.

Oh..This is really important point. Thank! I didn't remember the concept of input impedance. The is the actuall impedance the source impedance see.

Can I have one more question? In input impedance the electrical length βl is important and β is signal wavelength dependent. β is clear for continuous sinusoidal signal but what about single TTL signal? For example, 5 V High to Low signal with 10 us duration. How can I calculate β in this case? In other word, is input impedance is still clear for single shot signal?

 

[EM_Guy]

By Fourier analysis, any periodic signal can be decomposed into sines and cosines of various frequencies and amplitudes.

But when the characteristic impedance and load impedance both equal 50 ohms, the input impedance looking into the transmission line will not depend on $\beta l$ as you should verify.

 

[goodphy]

By Fourier analysis, any periodic signal can be decomposed into sines and cosines of various frequencies and amplitudes.

But when the characteristic impedance and load impedance both equal 50 ohms, the input impedance looking into the transmission line will not depend on $\beta l$ as you should verify.

Yes, that is right. I'm actually trying to make my understanding deeper. If I assume that I only have source impedance of High Z as a fixed value and single TTL (not periodic) is going in then electrical length is the parameter I can control the input impedance. (I'm not concerned of other ma

By Fourier analysis, any periodic signal can be decomposed into sines and cosines of various frequencies and amplitudes.

But when the characteristic impedance and load impedance both equal 50 ohms, the input impedance looking into the transmission line will not depend on $\beta l$ as you should verify.

Yes, you're right. I'm actually trying to understand how electrical length can be calculated in single TTL signal (not periodic) as it is trigger signal for our instrument. If I assume that my DG535 has fixed output impedance of High Z, then electrical length is the parameter I can control to make input impedance closely matched to High Z. Thus maybe I can Fourier-transform of single TTL signal and center frequency in the result is used for the calculation? I don't care of other matching technique here.

 

[EM_Guy]

A pulse excites a whole plethora of frequencies (for a finite amount of time).

I don't really understand your TTL signal. Can you describe it as a function of time?

The Fourier transform for a single flat pulse is a sinc function, meaning that the spectral content of the pulse is characterized by a sinc function in the frequency domain. Accordingly, you are exciting several different modes in your cable at the same time - each of which has its own $\beta$. The input impedance looking into the transmission line depends on $\beta$.

 

[goodphy]

A pulse excites a whole plethora of frequencies (for a finite amount of time).

I don't really understand your TTL signal. Can you describe it as a function of time?

The Fourier transform for a single flat pulse is a sinc function, meaning that the spectral content of the pulse is characterized by a sinc function in the frequency domain. Accordingly, you are exciting several different modes in your cable at the same time - each of which has its own $\beta$. The input impedance looking into the transmission line depends on $\beta$.

Yes, that single flat signal is TTL signal what I mean. So in this case with of sinc function in spectral domain is matter. I think I have goood info for this issue from you and can start to calculate some parameters. I really appreiciate your clear answer! Thanks again!

 

[sophiecentaur]

If you just want to eliminate pulse distortion / ringing that could be caused by a line, it is only necessary to match the load to the impedance of the line. If you match the source impedance to the line then you are wasting half of the power that you have generated and this could be a problem. Many times, it's best to make your source as low impedance as possible, for efficiency.

 

[Jeff Rosenbury]

There are several families of TTL. Do you know what family this is? (Likely the 74HC series, but there are other outputs on this equipment.) Then we can look up rise time, etc. What is the pulse width?

With this information we can answer EM_Guy's question, "I don't really understand your TTL signal. Can you describe it as a function of time?"

 

[the_emi_guy]

Goodphy,
You may be misunderstanding the output impedance control of the DG535. It can configured to accommodate either a 50 ohm load or a high impedance load. There is no selection for having its own output high impedance.

The DG535 output driver is designed to drive 50 ohms. When the user selects high Z, a FET turns on connecting a 50 ohm load across the output internally.

When you selected high Z, and also have an external 50 ohm load, you are double terminating the DG535 drive circuit. The distortion & low amplitude you are seeing is not caused by transmission line phenomena, but by the output driver struggling to drive 25 ohms.

 

[goodphy]

There are several families of TTL. Do you know what family this is? (Likely the 74HC series, but there are other outputs on this equipment.) Then we can look up rise time, etc. What is the pulse width?

With this information we can answer EM_Guy's question, "I don't really understand your TTL signal. Can you describe it as a function of time?"

Hello. I don't know how to classify our TTL signal but According to specification of DG535, rising time is extremely fast as ~2 or 3 ns. I've set pulse width of 10 us in time so in OSC measured clean TTL signal just looks single square pulse.

 

[goodphy]

Goodphy,
You may be misunderstanding the output impedance control of the DG535. It can configured to accommodate either a 50 ohm load or a high impedance load. There is no selection for having its own output high impedance.

The DG535 output driver is designed to drive 50 ohms. When the user selects high Z, a FET turns on connecting a 50 ohm load across the output internally.

When you selected high Z, and also have an external 50 ohm load, you are double terminating the DG535 drive circuit. The distortion & low amplitude you are seeing is not caused by transmission line phenomena, but by the output driver struggling to drive 25 ohms.

Hello.

I really appreciate your point!

The attached image is what I'd understood as a equivalent circuit for DG535 - BNC cable - Oscilloscope connection in my measurement. I guess you maybe right. I've misunderstood that Z_S is changeable output impedance (source impedance) of DG535.

Unfortunately, I still don't draw clear picture of what you have explained. Maybe I've stuck to my own picture too much..

Could you please give me picture of your reply? I think your reply is very important key to clear this long-term puzzling for me.

 

[Jeff Rosenbury]

That was a fine description of your output waveform. It is missing the (likely irrelevant) amplitude.

On page 28 of your manual, there's a section labeled IMPEDANCE CONTROL. It describes what happens when you use the "high Z" output feature. Essentially it switches in a 50Ω resistor in series with Z_S and in parallel with Z₀, as The_emi_guy stated. It is intended for use with test equipment with high impedance inputs like scopes, so you don't have to carry your own 50Ω terminator.

Using it to feed a 50Ω line will cause a 25Ω mismatch at that point.

All of those details are in the manual for a reason. Learn them. Love them.

 

[goodphy]

That was a fine description of your output waveform. It is missing the (likely irrelevant) amplitude.

On page 28 of your manual, there's a section labeled IMPEDANCE CONTROL. It describes what happens when you use the "high Z" output feature. Essentially it switches in a 50Ω resistor in series with Z_S and in parallel with Z₀, as The_emi_guy stated. It is intended for use with test equipment with high impedance inputs like scopes, so you don't have to carry your own 50Ω terminator.

Using it to feed a 50Ω line will cause a 25Ω mismatch at that point.

All of those details are in the manual for a reason. Learn them. Love them.

The amplitude is 4 V, anyway. Thanks for giving me answer.

But still, I don't get the picture of what happens on the DG535 output circuit when I selects High Z and 50 Ohm.

I've just gotten that Z_S is not something changed to be either High Z or 50 Ohm from my choice. Could you make it detailed of your mention "when you use the "high Z" output feature. Essentially it switches in a 50Ω resistor in series with ZS and in parallel with Z0"? What is switched and what are in series with 50 Ω and parallel with Z₀? Could you give me simple drawing?

I'm sorry but I need more assistance to reach ultimate understanding.

 

[the_emi_guy]

goodphy,
Don't bother with trying to draw a schematic of the driver. It is not a voltage source with series resistor, nor is it a standard logic gate.

Consider it a black box that wants to have its output loaded with 50 ohms. You can provide the 50 ohm load externally (your scope), or you can have it supply the 50 ohm load internally by selecting the impedance control to high z. When you did both the driver was loaded with 25 ohms.

 

[sophiecentaur]

Consider it a black box that wants to have its output loaded with 50 ohms.

That's an excellent way to approach most of electronic design. You just don't have time to worry about all the details because you can't be sure which are the most relevant. Plenty of people, cleverer than you and me have been involved in the design of these beasts and the units usually obey the spec - you just need to read it right.
That statement is not a cop-out. It is the way our brains work with most other problems. There will be occasions where it does't turn out to be that simple but worry about them when they actually turn up.