This article was first published on the Sierra Circuits blog.
It is the second of the PCB Transmission Line series and follows the article entitled What is a PCB transmission line? It was written with the great help of Atar Mittal, Sierra’s Electrical Engineer and General Manager.
At high frequencies, transmission lines need to have a controlled impedance to predict the behavior of the signals and avoid signal reflections, crosstalk, electromagnetic noise, etc. which could damage the signal quality and cause errors.
This is the reason why you need to know at which speed signals propagate on transmission lines and the time they take to do so. I will give you a few equations to calculate the signal speed and the propagation delay for both striplines and microstrips.
Signal speed
Let’s first discuss the speeds at which signals propagate on a PCB interconnect.
Electromagnetic signals travel in vacuum (or air) at the same speed as of light, which is:
A signal travels on a PCB transmission line at a slower speed, affected by the dielectric constant (Er) of the PCB material – the relations for calculating the signal speed on a PCB are given below:
The Group Delay also requires care, but in general it describes the delay of energy transport through the system at that particular frequency. The following examples show what happens for a pure delay (Fig. 1), a pure delay with a 180° phase shift (inversion) (Fig. 2), a pure delay and a.
Where:
- Vc is the velocity of light in vacuum or air
- Er is the dielectric constant of the PCB material
- Ereff is the effective dielectric constant for microstrips; its value lies between 1 and Er, and is approximately given by:
Thus, the speeds of signals on a PCB is less than that in air. If Er equals about 4 (like for FR4 material types), then the speed of signals on a stripline is half that in air, i.e. it is about 6 in/ns.
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Henceforth, you can use Vp to denote the speed of signals on a PCB.
Propagation delay (tpd)
![Signal Signal](https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Delay-line_block_diagram.png/220px-Delay-line_block_diagram.png)
The propagation delay is the time taken by a signal to propagate over a unit length of the transmission line:
The DSP(digital signal processing) will impart a signal delay usually measured in milliseconds. A common delay would be 5 milliseconds. The speed of sound is (roughly) one foot per millisecond. So a 5 millisecond delay will cause your receiver to set the distance setting about 5 feet more than the physical distances involved. Try applying 3 different times from the delay calculator to a LCR delay. Delay calculator time – Applied Usage. I also suggest using the time calculated from the delay calculator to be used as the entire time Say you use the delay calculator and calculate a time of 600ms from a BPM of 100. You decide to apply this to a reverb, and use a. If a speaker impedance rating is 4-ohms, that speaker is typically a high-end, audiophile speaker that needs an amplifier that has the ability to provide more power. This is just a simple fact. A loudspeaker producer will likely build a 4-ohm speaker be he knows what type of amplifier would be needed for it to get the appropriate sound. Delay in milliseconds = distance in cm / 34.3; Delay in milliseconds = distance in inches / 13.5; Alternatively, if you have an acoustic measurement program, you can calculate the delay by measuring the arrival time of the signal from each driver, and calculating the difference. The result is the time delay needed.
Where:
- V is the signal speed in the transmission line
In vacuum or air, it equals 85 picoseconds/inch (ps/in).
On PCB transmission lines, the propagation delay is given by:
The signal speeds and propagation delays for a few PCB materials are given in the table below:
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The next article of this PCB Transmission Line series will focus on controlled impedance. It will answer the question: When is the length of an interconnection to be considered as a controlled impedance transmission line?
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