Impedance of a trace in PCB

Hi, I am wondering how the impedance of the trace on the PCB does not depend on the length but it only depend on the trace width for a given stack up setting. If we increase the trace width, the impedance of single ended trace will decrease for a given stack up setting. Is this impedance is somehow related to sheet resistance in ohms which does not depend how big is the square ? Second question is, the impedance which we maintain for example 50 ohm for a single ended trace for a given stack up setting, is DC or AC impedance ? I do not see any frequency setting in the stack up editor which calculate the trace width for a target impedance.

Transmission line impedance is an AC quantity, it's not related to sheet resistance. Impedance of a lossless transmission line is

Z = √(L'/C')

L' and C' being the specific inductance and capacitance per length unit. As they are frequency independent in a first order, Z is frequency independent, too.

I have used Mentor Graphics xDx Designer and PCB Expedition tools. I do not think I ever enter any frequency range while calculating trace width which can give 50 ohm impedance for a given stack up setting.

FvM said:

Transmission line impedance is an AC quantity, it's not related to sheet resistance. Impedance of a lossless transmission line is Z = √(L'/C')

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This is the formula for a transmission line.

However, the impedance of the trace on a PCB may be something else. Individual traces have their own capacitance and inductance values.

Are you sure individual traces on a PCB can be considered as transmission lines?

In the attachment you can see that in the Stack up Editor, I can calculate trace width for single ended trace that gives 50 ohm impedance for a given stack up settings. Also for differential LVDS signals the tool can calculate the trace width and spacing for 100 ohm impedance for a given stack up setting. There is no field where I can enter frequency information.

Sorry, I did not notice the "stack up"- right. The trace along with the layer below forms the transmission line. Just like a coax.

c_mitra said:

Sorry, I did not notice the "stack up"- right. The trace along with the layer below forms the transmission line. Just like a coax.

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I still have same question. The target impedance which we set in the stack up editor for single and differential pair is based on the spacing between the layers, and dielectric material but how the target impedance related to frequency ? If it is AC impedance then it would not be constant over the frequency but the tool shows 50 ohm as target impedance for single ended and 100 ohm as target impedance for differential pair.

See post #2.

Unless the frequency is very low (when you ignore something; I have forgotten), the impedance of the transmission line is constant and independent of the AC frequency.

If the impedance is 50 Ohm and you put 100V at 50Hz, it will not take 2A current. But frankly speaking, I have forgotten much.

If it is AC impedance then it would not be constant over the frequency but the tool shows 50 ohm as target impedance for single ended and 100 ohm as target impedance for differential pair.

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The problem is that you simply don't understand what transmission impedance means. It's a basically frequency independent quantity. I don't think that it's useful to retell transmission line theory in this thread. You better read a RF engineering text book or tutorial.

Unless the frequency is very low (when you ignore something; I have forgotten), the impedance of the transmission line is constant and independent of the AC frequency.

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The impedance as calculated in post #2 is still constant for low frequency, but if the transmission is shorter than e.g. 1/10 of wavelength, you don't see transmission line related effects, just some lumped parallel capacitance and series inductance.

This means for 10 MHz there will be no transmission line effect if the length is less then 3 m (1/10 of wavelength) but for 1 GHz where 1/10 wavelength is 30 mm, there will be transmission line effect if the length is greater then 30 mm. I understand that the transmission line impedance is a frequency dependent quantity (Zo = sqrt (L'/C'), but I do not understand what the target impedance 50 ohm (single ended) and 100 ohm (LVDS) shows in the stack up editor which I have attached in one previous post.

Transmission lines with specific impedance are used in RF and fast digital electronic systems to transport signals with high quality. Signal transmission over 100 ohm differential pairs is common to many fast interfaces like SATA, PCIe, Ethernet or HDMI. The line impedance needs to be kept constant along the signal path through PCB traces, connectors and cable, otherwise signal reflections take place.

Yes this was my main question. At one side we say that the line impedance need to be kept constant along the signal path through PCB traces and to achieve this, stack up editor can calculate trace width for target impedance and for a given setting of layers stack up. The line impedance constant means constant impedance for all frequencies ? right ? because PCB traces are transmission line either micro strip or strip line ? But on the other hand we know that the impedance of the transmission line is a frequency dependent which depend on C per length and L per length. Any simple expatiation on these two concepts ?

C of PCB substrate is only slightly frequency dependent, L is not frequency dependent at all unless you consider skin effect. Why are you harping on about frequency effects?

Characteristic impedance is determined by distance between a trace and its return, or for diff pairs two traces and return path. loop area

FvM said:

C of PCB substrate is only slightly frequency dependent, L is not frequency dependent at all unless you consider skin effect. Why are you harping on about frequency effects?

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C of PCB substrate is not a meaningful concept. A capacitor is made of a pair of conductors separated by a dielectric which stores the energy. The capacitance in the ideal case is frequency independent but the capacitative impedance is frequency dependent. Capacitative energy is stored in the electric field. Similarly the energy stored into the inductor.

I too had the same confusion in the beginning. Transmission line impedance refers to a parallel pair of conductors (and their relative capacitance and inductance) and they have their own characteristic impedance.

I confused impedance of individual traces (individual traces too have capacitance and inductance).

c_mitra said:

C of PCB substrate is not a meaningful concept. A capacitor is made of a pair of conductors separated by a dielectric which stores the energy. The capacitance in the ideal case is frequency independent but the capacitative impedance is frequency dependent. Capacitative energy is stored in the electric field. Similarly the energy stored into the inductor.

I too had the same confusion in the beginning. Transmission line impedance refers to a parallel pair of conductors (and their relative capacitance and inductance) and they have their own characteristic impedance.

I confused impedance of individual traces (individual traces too have capacitance and inductance).

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The characteristic impedance depends on the material dielectric constant and the capacitance per length of the trace. Here is the formula for characteristic impedance Zo = 83/C' sqrt (er). Making the signal trace wider in microstrip will increase the capacitance per length which means characteristic impedance decrease. This shows that the characteristic impedance does not depends on the trace length. For FR4 the dielectric is around 4, when the trace width is twice the dielectric thickness, the characteristic impedance is about 50 Ohms.

I am wondering how does this characteristic impedance depends on the frequency ?

Second question, when we use 1 meter of RG58 cable having 50 ohm characteristic impedance with 50 ohm BNC connector with a signal generator. This characteristic impedance 50 ohm is not the resistance of the RG58 ? because when we measure resistance of the 1 meter RG58 using ohm meter, it shows 0.2 ohm not 50 ohm. On the other hand, if the source impedance is 50 ohm and the load impedance is also 50 ohm we get the half voltage signal when we measure on the on the load resistance, this is because of voltage divider rule, as the source internal resistance and the load resistance are both 50 ohm in series. This shows that the resistance of the RG58 in calculation is 0.2 ohm which does not effect much in series but where is the characteristics impedance 50 ohm of the cable RG58 in calculation ?

expertengr said:

Second question, when we use 1 meter of RG58 cable having 50 ohm characteristic impedance with 50 ohm BNC connector with a signal generator. This characteristic impedance 50 ohm is not the resistance of the RG58 ? because when we measure resistance of the 1 meter RG58 using ohm meter, it shows 0.2 ohm not 50 ohm. On the other hand, if the source impedance is 50 ohm and the load impedance is also 50 ohm we get the half voltage signal when we measure on the on the load resistance, this is because of voltage divider rule, as the source internal resistance and the load resistance are both 50 ohm in series. This shows that the resistance of the RG58 in calculation is 0.2 ohm which does not effect much in series but where is the characteristics impedance 50 ohm of the cable RG58 in calculation ?

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The impedance is to be measured between the central conductor and the screen sleeve at a frequency sufficiently high so that the length of the cable is large compared to the wavelength of the signal. For 50/60Hz signals the cables have to be kms of length and for this particular case, the frequency will be of the GHz range.

At lower frequency, the impedance will be very high and and can be ignored. You do not use a coaxial cable for DC (but it is very useful to shield high frequency noise that are practically shorted).

This means characteristics impedance of RG58 has to be measured between signal and ground ? that gives 50 ohm ?

expertengr said:

This means characteristics impedance of RG58 has to be measured between signal and ground ? that gives 50 ohm ?

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Exactly! The source driving the cable will see this impedance and to prevent reflection, the load should be connected and that too will see an impedance of 50 Ohm. In this ideal case we consider no reflection.