# Impedance on BNC Cable

#### mig78

Joined Mar 30, 2006
8
Hi,

I have been trying to measure the impedance of a normal 50Ohm BNC cable but i get an open reading.

I probed the positive lead to the center connector while the negative lead to the ground (outer surface) of coaxial cable.

Can someone pls advice what is the proper way of measuring them.
Appreciate some feedback

Thanks.

#### paultwang

Joined Mar 8, 2006
80
You have to .. uh... connect the other end? After all, it is a cable.

Connect the other end of the BNC cable to a known passive resistance.

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by paultwang@Apr 6 2006, 09:49 AM
You have to .. uh... connect the other end? After all, it is a cable.

Connect the other end of the BNC cable to a known passive resistance.
[post=15898]Quoted post[/post]​
WRONG on both counts.

It's a coaxial cable, BNC is the type of connector.

If I terminate the cable with 200 ohms and use an ohmmeter I'll measure 200 ohms and not 50 ohms.

The 50 Ohms is the MAGNITUDE of the characteristic IMPEADANCE of the cable. Characteristic IMPEADANCE is a complex number and cannot be measured with an ohmmeter. The cable can be terminated or not, and measured with a network analyzer which will give you the complex impeadance measurement as a function of frequency over any range you care to pay for. The very best network analyzers cost just north of USD \$100,000.00, maybe slightly less on ebay.

If you are interested, characteristic impeadance is actually one of the constants that arises in the solution of the partial differential equation of an ideal transmission line modeled as ditributed inductance and capacitence. It depends on these distributed parameters, and on the geometry of the cable, the so called boundry conditions of the problem.

As a practical matter we terminate a transmission line with a resistor, that has a complex impeadance of 50 ohms, and zero for an imaginary part. This will minimize the power reflected back to the source, and maximize the power transferred to the load.

Your homework problem is to tell me how many complex numbers there are with a MAGNITUDE of 50. A termination resistor of 50 ohms, which we can write as 50 + j0 is one of them. How many others can you think of?

#### n9xv

Joined Jan 18, 2005
329
Yep!

#### windoze killa

Joined Feb 23, 2006
605
Originally posted by mig78@Apr 6 2006, 10:54 PM
Hi,

I have been trying to measure the impedance of a normal 50Ohm BNC cable but i get an open reading.

I probed the positive lead to the center connector while the negative lead to the ground (outer surface) of coaxial cable.

Can someone pls advice what is the proper way of measuring them.
Appreciate some feedback

Thanks.
[post=15895]Quoted post[/post]​
Impedence of any transmission line as papabravo said cannot be measured without some expensive equipment. The characteristic imepedence is made up of series inductance and parallel capactiance. It all has to do with the diameter of the conductors, the space between them, the dielectric between them and the material they are made of.

The only cheap way of measuring it would be to get a standing wave meter or a meter capable of measuring reflected power. Apply an RF power source to one end and you terminate the cable with a variable load and adjust it for zero refelcted power. Then you should be able to measure the load resistance and this should be equal to the impedence af the cable.

PS. the variable load should be purley resistive. ie. not a wire wound potentiometer.

#### mig78

Joined Mar 30, 2006
8
I really appreciate all the valuable feedback. Now I got them to some extend. I guess I have to go & revise back my Transmission Line theory which have been totally wiped out...

Thanks Guys!

#### Dave

Joined Nov 17, 2003
6,970
I recall at University performing a Transmission Line experiment, where we mocked up an artificial transmission line using a distributed-model of approximately 6000m (obviously it wasn't that big in reality!!). One of the objectives of the experiment was to deduce the characteristic impedance of the TM line and see if we could accurately ascertain the length of the TM line by analytical methods. To measure the characteristic impedance of the TM line we developed a variable impedance circuit at the TM line output which we varied to until there were no reflections along the TM line, from which we could measure the magnitude of the impedance and hence the characteristic impedance of the TM line. We managed to achieve this with very little technical equipment or expense and we were shocked to see that the length could be analytically derived to within a couple of percent.

This experiment was merely a proof of concept for modelling long TM lines in a laboratory environment with minimum cost.

Anyhow, for more information about TM lines and the theory refer to AAC: Volume 2 Chapter 13.

Dave

#### n9xv

Joined Jan 18, 2005
329
There is a way to measure the impedance of a transmission line with reasonable accuracy using a scope and signal generator. Connect the signal generator to the transmission line. Connect a termination load across the opposite end of the transmission line. With the scope, measure the voltage across the signal generator output when connected to the transmission line & load. Then, measure the voltage across the load. Now, subtact the "load voltage" from the "generator voltage". The result is the voltage across the transmission line. Now, work the problem like a proportion;

TML means transmission line,

so,

The transmission line & load connected across the generator constitutes a series circuit. In this mannor we can use Kirchoff's voltage law that states, "the sum of all voltage drops in a series circuit must equal the applied voltage". In other words, the resistances are proportional to the voltages across them. With this method, We can "treat" the transmission line as a simple resistor. All we are interested in is the level of impedance. The characteristic impedance of the feedline is that level of impedance that will be exhibited by the feedline at any frequency within the specified range of the feedline. If the feedline is designated for use at VHF/UHF frequencies for instance, then the feedline will exhibit a characteristic impedance of rated-ohms throughout that entire range of frequencies.

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by n9xv@Apr 7 2006, 09:03 AM
There is a way to measure the impedance of a transmission line with reasonable accuracy using a scope and signal generator. Connect the signal generator to the transmission line. Connect a termination load across the opposite end of the transmission line. With the scope, measure the voltage across the signal generator output when connected to the transmission line & load. Then, measure the voltage across the load. Now, subtact the "load voltage" from the "generator voltage". The result is the voltage across the transmission line. Now, work the problem like a proportion;

TML means transmission line,

so,

The transmission line & load connected across the generator constitutes a series circuit. In this mannor we can use Kirchoff's voltage law that states, "the sum of all voltage drops in a series circuit must equal the applied voltage". In other words, the resistances are proportional to the voltages across them. With this method, We can "treat" the transmission line as a simple resistor. All we are interested in is the level of impedance. The characteristic impedance of the feedline is that level of impedance that will be exhibited by the feedline at any frequency within the specified range of the feedline. If the feedline is designated for use at VHF/UHF frequencies for instance, then the feedline will exhibit a characteristic impedance of rated-ohms throughout that entire range of frequencies.
[post=15941]Quoted post[/post]​
I agree that you can measure the impeadance of a coaxial cable at a single frequency with lab equipment that is within the budget of most experimenters. What you cannot do quickly, without the high priced network analyzers is measure impeadance as a FUNCTION of frequency. The former measurement has the unfortunate tendency to lead to the conclusion that characteristic impeadance is a CONSTANT, which it most definitely is not. It changes in strange an unusual ways as the frequency increases, first becoming innductive, then less so, then crossing the real axis and becoming capacitive, then less so, then crossing the real axis again, and so on, like a helpless raft circling a whirlpool.

#### n9xv

Joined Jan 18, 2005
329
An alternate method can be used to measure the characteristic impedance of transmission line cable without the necessity of a load termination.

This can be done using voltage levels.

Vs = source voltage
VLoc = load voltage open circuit
VLsc = load voltage short circuit
Zs = source or generator internal impedance
ZL = load impedance (characteristic impedance)

Note the the value of "open circuit" voltage of the generator. This is Vs.

Connect the generator to the cable and leave the opposite end open. Measure the voltage across the generator. This is VLoc.

Then, connect the generator to the cable and short the opposite end. This is VLsc.

Zs is a specification given for the particular generator. Its the generator's internal impedance.

Now, do the following calculations;

OPEN CIRCUIT impedance = (VLoc X Zs) / (Vs - VLoc)

SHORT CIRCUIT impedance = (VLsc X Zs) / (Vs - VLsc)

Then,

the final calculation for characteristic impedance is,

SQUARE ROOT OF (SHORT CIRCUIT impedance X OPEN CIRCUIT impedance)

Papabravo, why do you say that characteristic impedance is not a constant. It is indeed a constant. Thats the "characteristic" of characteristic impedance. The impedance remains constant (within specified ratings of a given cable) over a vast range of frequencies.

Example:

Let say a given cable is rated a 50-ohms with frequency specs of DC to 1-GHz. BTW, I use cable of similar specs for transmission line in Amatuer Radio. Namely, RG-8U, Belden 9913 or their varous equivalents. This cable retains the characteristic impedance of 50-ohms whether I use it with a 1.8-MHz transceiver or a transceiver operating at 440-MHz. A typical Amatuer transceiver or "rice box" as there're affectionately called, covers 1.8-MHz to 440-MHz. It has an SO-239 or type-N antenna output connector rated at 50-ohms. 50-ohm cable can be used over the entire range of frequencies. If the characteristic impedance changed as frequency changed then the cable would not be very versitile or practical. The cable acts as a complex band pass filter. It will pass RF energy up to a pre-determined design point and will then sharply cuttoff above those frequencies.

Then along comes the wave-guide . . .

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by n9xv@Apr 7 2006, 11:21 AM
An alternate method can be used to measure the characteristic impedance of transmission line cable without the necessity of a load termination.

This can be done using voltage levels.

Vs = source voltage
VLoc = load voltage open circuit
VLsc = load voltage short circuit
Zs = source or generator internal impedance
ZL = load impedance (characteristic impedance)

Note the the value of "open circuit" voltage of the generator. This is Vs.

Connect the generator to the cable and leave the opposite end open. Measure the voltage across the generator. This is VLoc.

Then, connect the generator to the cable and short the opposite end. This is VLsc.

Zs is a specification given for the particular generator. Its the generator's internal impedance.

Now, do the following calculations;

OPEN CIRCUIT impedance = (VLoc X Zs) / (Vs - VLoc)

SHORT CIRCUIT impedance = (VLsc X Zs) / (Vs - VLsc)

Then,

the final calculation for characteristic impedance is,

SQUARE ROOT OF (SHORT CIRCUIT impedance X OPEN CIRCUIT impedance)

Papabravo, why do you say that characteristic impedance is not a constant. It is indeed a constant. Thats the "characteristic" of characteristic impedance. The impedance remains constant (within specified ratings of a given cable) over a vast range of frequencies.

Example:

Let say a given cable is rated a 50-ohms with frequency specs of DC to 1-GHz. BTW, I use cable of similar specs for transmission line in Amatuer Radio. Namely, RG-8U, Belden 9913 or their varous equivalents. This cable retains the characteristic impedance of 50-ohms whether I use it with a 1.8-MHz transceiver or a transceiver operating at 440-MHz. A typical Amatuer transceiver or "rice box" as there're affectionately called, covers 1.8-MHz to 440-MHz. It has an SO-239 or type-N antenna output connector rated at 50-ohms. 50-ohm cable can be used over the entire range of frequencies. If the characteristic impedance changed as frequency changed then the cable would not be very versitile or practical. The cable acts as a complex band pass filter. It will pass RF energy up to a pre-determined design point and will then sharply cuttoff above those frequencies.

Then along comes the wave-guide . . .
[post=15946]Quoted post[/post]​
I agree that the characteristic impeadance has a mean value with a small variance over a wide range of frequencies, but what is the characteristic impeadance of the cable and the connectors at 10 GHz, at 100 GHz., at 1 Thz. I think you will find RG-8U and SO-239 connectors quite useless at those frequencies since the cable dimensions are becoming a significant fraction of the wavelength.

I was a bit sloppy in my previous descriptions. What I meant was that when you measure the actual imeadance of a particular piece of cable in a particular configuration it changes as a function of frequency and its geometry. In measuring an actual cable there are also non-reactive losses that come into play.

The first derivation of characteristic impeadance assumes distributed reactive impeadances only and that the dimensions of the cable are small with respect to the wavelength.

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by n9xv@Apr 7 2006, 11:21 AM
An alternate method can be used to measure the characteristic impedance of transmission line cable without the necessity of a load termination.

This can be done using voltage levels.

Vs = source voltage
VLoc = load voltage open circuit
VLsc = load voltage short circuit
Zs = source or generator internal impedance
ZL = load impedance (characteristic impedance)

Note the the value of "open circuit" voltage of the generator. This is Vs.

Connect the generator to the cable and leave the opposite end open. Measure the voltage across the generator. This is VLoc.

Then, connect the generator to the cable and short the opposite end. This is VLsc.

Zs is a specification given for the particular generator. Its the generator's internal impedance.

Now, do the following calculations;

OPEN CIRCUIT impedance = (VLoc X Zs) / (Vs - VLoc)

SHORT CIRCUIT impedance = (VLsc X Zs) / (Vs - VLsc)

Then,

the final calculation for characteristic impedance is,

SQUARE ROOT OF (SHORT CIRCUIT impedance X OPEN CIRCUIT impedance)

Papabravo, why do you say that characteristic impedance is not a constant. It is indeed a constant. Thats the "characteristic" of characteristic impedance. The impedance remains constant (within specified ratings of a given cable) over a vast range of frequencies.

Example:

Let say a given cable is rated a 50-ohms with frequency specs of DC to 1-GHz. BTW, I use cable of similar specs for transmission line in Amatuer Radio. Namely, RG-8U, Belden 9913 or their varous equivalents. This cable retains the characteristic impedance of 50-ohms whether I use it with a 1.8-MHz transceiver or a transceiver operating at 440-MHz. A typical Amatuer transceiver or "rice box" as there're affectionately called, covers 1.8-MHz to 440-MHz. It has an SO-239 or type-N antenna output connector rated at 50-ohms. 50-ohm cable can be used over the entire range of frequencies. If the characteristic impedance changed as frequency changed then the cable would not be very versitile or practical. The cable acts as a complex band pass filter. It will pass RF energy up to a pre-determined design point and will then sharply cuttoff above those frequencies.

Then along comes the wave-guide . . .
[post=15946]Quoted post[/post]​
I agree that the characteristic impeadance has a mean value with a small variance over a wide range of frequencies, but what is the characteristic impeadance of the cable and the connectors at 10 GHz, at 100 GHz., at 1 Thz. I think you will find RG-8U and SO-239 connectors quite useless at those frequencies since the cable dimensions are becoming a significant fraction of the wavelength.

I was a bit sloppy in my previous descriptions. What I meant was that when you measure the actual imeadance of a particular piece of cable in a particular configuration it changes as a function of frequency and its geometry. In measuring an actual cable there are also non-reactive losses that come into play.

The first derivation of characteristic impeadance assumes distributed reactive impeadances only and that the dimensions of the cable are small with respect to the wavelength. So the coaxial cable becomes....a waveguide, inductors become capacitors and vice versa.

#### n9352527

Joined Oct 14, 2005
1,198
Originally posted by Papabravo@Apr 7 2006, 05:08 PM
... inductors become capacitors and vice versa.
[post=15948]Quoted post[/post]​
What are the physical phenomenon/mechanisms that govern these changes?

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by n9352527@Apr 7 2006, 12:29 PM
What are the physical phenomenon/mechanisms that govern these changes?
[post=15949]Quoted post[/post]​
The physics is that the wave length of the signal and the dimensions of the component are the same order of magnitude. Take an inductor wound on PVC pipe with #26 magnet wire with the turns adjacent to each other. At each point around the wire there is an adjacent wire which forms a little capacitor. At a certain wave length these distributed little capacitors begin to influence the impeadance of the inductor and it starts to look like a capacitor.

Foa a capacitor with circular parallel plates, as the frequency is increased, the field ceases to be uniform in the region between the plates. There is a Bessel Function in the expression for the electric field which goes to zero at the edge of the circular plates at some frequency. At this frequency it is like there was a short circuit all the way around the edge even though there is no conductor there. As you keep going up in frequency you get opposition to the flow of current which makes it start to look like an inductor.

I first encountered this description in Feynman, Volume II

#### n9352527

Joined Oct 14, 2005
1,198
Originally posted by Papabravo@Apr 7 2006, 06:59 PM
The physics is that the wave length of the signal and the dimensions of the component are the same order of magnitude. Take an inductor wound on PVC pipe with #26 magnet wire with the turns adjacent to each other. At each point around the wire there is an adjacent wire which forms a little capacitor. At a certain wave length these distributed little capacitors begin to influence the impeadance of the inductor and it starts to look like a capacitor.

Foa a capacitor with circular parallel plates, as the frequency is increased, the field ceases to be uniform in the region between the plates. There is a Bessel Function in the expression for the electric field which goes to zero at the edge of the circular plates at some frequency. At this frequency it is like there was a short circuit all the way around the edge even though there is no conductor there. As you keep going up in frequency you get opposition to the flow of current which makes it start to look like an inductor.

I first encountered this description in Feynman, Volume II
[post=15950]Quoted post[/post]​
Was that Feynman Lecture on Cavity Resonators, Volume II, Chapter 23?

I was under the impression that the treatments presented by Feynman there were for physically adjacent turns of wire for inductor and parallel plates with radial edges for capacitor. Are these treatments extensible to transmission lines which have different physical constructions (for example, no adjacent turns or parallel plate edges)?

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by n9352527@Apr 7 2006, 07:16 PM
Was that Feynman Lecture on Cavity Resonators, Volume II, Chapter 23?

I was under the impression that the treatments presented by Feynman there were for physically adjacent turns of wire for inductor and parallel plates with radial edges for capacitor. Are these treatments extensible to transmission lines which have different physical constructions (for example, no adjacent turns or parallel plate edges)?
[post=15961]Quoted post[/post]​
Volume II, chapter 23 is correct for the behavior of real inductors and capacitors at very high frequencies.

Section 22-6 describes a ladder network and how the propagation is flat out to some frequency and then falls off very rapidly. See Figure 22-22. Ladder networks are used in the low frequency analysis of transmission lines.

In section 24-3 it is explained that for wave guides when the wave number k becomes imaginary we no longer have propagation down the guide but exponetially decaying fields which don't go very far down the guide at all.

Section 24-1 on transmission lines has two assumptions:

a. there are no dielectrics or magnetic materials in the space between the conductors
b. the currents are all on the surfaces of the conductors

and two results. The first is that L_sub_zero times C_sub_zero is always 1/c^2 for ANY parallel pair of conductors. The second is that characteristic impeadance is indeed a constant for these ideal coaxial cables.

From Gonzalez p.143 we find that effective dielectric constant has a definite effect on the characteristic impeadance of microstriplines. The determination of this effective dielectric constant turns out to be valid for the lower microwave range only. Since most coaxial cables are fabricated with a dielectric between the inner and outer conducter I'm going to make a stretch and say that Feynman's assumtion a) above is violated and the characteristic impeadance computed at some low frequency is no longer valid beyond some cutoff frequency.

If I've made any errors in this or previous posts then I apologize for any confusion.

#### windoze killa

Joined Feb 23, 2006
605
Originally posted by Papabravo@Apr 8 2006, 11:34 AM
Volume II, chapter 23 is correct for the behavior of real inductors and capacitors at very high frequencies.

Section 22-6 describes a ladder network and how the propagation is flat out to some frequency and then falls off very rapidly. See Figure 22-22. Ladder networks are used in the low frequency analysis of transmission lines.

In section 24-3 it is explained that for wave guides when the wave number k becomes imaginary we no longer have propagation down the guide but exponetially decaying fields which don't go very far down the guide at all.

Section 24-1 on transmission lines has two assumptions:

a. there are no dielectrics or magnetic materials in the space between the conductors
b. the currents are all on the surfaces of the conductors

and two results. The first is that L_sub_zero times C_sub_zero is always 1/c^2 for ANY parallel pair of conductors. The second is that characteristic impeadance is indeed a constant for these ideal coaxial cables.

From Gonzalez p.143 we find that effective dielectric constant has a definite effect on the characteristic impeadance of microstriplines. The determination of this effective dielectric constant turns out to be valid for the lower microwave range only. Since most coaxial cables are fabricated with a dielectric between the inner and outer conducter I'm going to make a stretch and say that Feynman's assumtion a) above is violated and the characteristic impeadance computed at some low frequency is no longer valid beyond some cutoff frequency.

If I've made any errors in this or previous posts then I apologize for any confusion.
[post=15963]Quoted post[/post]​
Thats the way. Quote left handed brail at us. Can't anyone speak English anymore. ;-)

#### pebe

Joined Oct 11, 2004
626
Originally posted by windoze killa@Apr 8 2006, 07:23 AM
Thats the way. Quote left handed brail at us. Can't anyone speak English anymore. ;-)
[post=15966]Quoted post[/post]​
The topic serms to have deviated from cable to waveguides, hasn't it? May I confirm in plain English the properties of characteristic impedance of a cable?

1. You cannot measure the characteristic impedance of a cable by measuring the DC resistance between inner and outer conductors  it is a measure of how the cable reacts to an applied AC signal.
2. It is resistive over the range of frequencies the cable was designed for.
3. It has a constant value over that range.
4. It is unaffected by the length of cable.
5. It is unaffected by the DC resistance of the conductors.
6. If you terminate the end of a cable with a resistive load equal to the characteristic impedance of the cable and feed it from a signal source, then the input end of that cable will appear to the source as though that value of resistance was connected instead.

#### Papabravo

Joined Feb 24, 2006
14,859
Originally posted by pebe@Apr 9 2006, 02:10 PM
The topic serms to have deviated from cable to waveguides, hasn't it? May I confirm in plain English the properties of characteristic impedance of a cable?

1. You cannot measure the characteristic impedance of a cable by measuring the DC resistance between inner and outer conductors  it is a measure of how the cable reacts to an applied AC signal.
2. It is resistive over the range of frequencies the cable was designed for.
3. It has a constant value over that range.
4. It is unaffected by the length of cable.
5. It is unaffected by the DC resistance of the conductors.
6. If you terminate the end of a cable with a resistive load equal to the characteristic impedance of the cable and feed it from a signal source, then the input end of that cable will appear to the source as though that value of resistance was connected instead.
[post=16011]Quoted post[/post]​
I agree, that is a reasonable summary of the thread. A thread which deviates is not always a bad thing. I think I discovered a bit more than I knew off the top of my head in the process which IMHO is always a good thing. The essential thing I discovered was, the effect of the dielectric used in the actual cable construction may be more important then I realized. This is especially true as you try to push the envelope which we all like to do.

#### windoze killa

Joined Feb 23, 2006
605
Originally posted by Papabravo@Apr 8 2006, 11:34 AM
Section 24-1 on transmission lines has two assumptions:

a. there are no dielectrics or magnetic materials in the space between the conductors
b. the currents are all on the surfaces of the conductors

and two results. The first is that L_sub_zero times C_sub_zero is always 1/c^2 for ANY parallel pair of conductors. The second is that characteristic impeadance is indeed a constant for these ideal coaxial cables.

From Gonzalez p.143 we find that effective dielectric constant has a definite effect on the characteristic impeadance of microstriplines. The determination of this effective dielectric constant turns out to be valid for the lower microwave range only. Since most coaxial cables are fabricated with a dielectric between the inner and outer conducter I'm going to make a stretch and say that Feynman's assumtion a) above is violated and the characteristic impeadance computed at some low frequency is no longer valid beyond some cutoff frequency.

[post=15963]Quoted post[/post]​
Firstly, my previous comment was meant in humour.

I taught transmission lines and RF fundamentals for a few years. One thing I must point out about the quotes above is that they refer to the "perfect" transmission line. Of course the is no such thing but we need a starting point.

A point about wave guides. They are more or less the same as any other transmission line. Because of the frequency that they are used at they rely totally on skin effect, that wonderful thing that stops solid conductor coax from working well at really high frequencies.

Another thing a lot of people forget about in RF design is velocity factor and propagation delay. Due to phase shifts through the imaginary LC circuits in a transmission line there is a delay over the length of the line.