Impulse timetable

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The pulse schedule ( English diagram Lattice , also shaft schedule ) is a graphical method to the temporal course of a voltage jump along an electric line to follow. The aim is to understand and calculate the resulting curve shape as a result of the reflections at the cable ends.

background

For example, if lightning strikes an overhead line , a high-voltage pulse travels as a traveling wave at high speed to both ends of the line and is reflected there because of the mismatch that normally occurs . The same applies to this reflected portion: it also runs to the other end of the line and can be reflected again there. Depending on the reflection factor, phase and amplitude can change and the voltage jumps become smaller and smaller. In the case of practically structured overhead lines, the surge arresters attached to the ends of the lines to avoid overvoltage cause partial absorption.

In the case of a data bus that connects the components of a computer, suitable terminating resistors must be used to ensure that no disruptive pulse reflections can occur. If exactly two components are to be connected, unwanted reflections can easily be avoided. However, as soon as several “consumers” have to be connected at different points on the line, signal reflections can occur at each branch, for which pulse timetables have been developed.

Graphical representation

If the load resistance is less than Z , the voltage jump is reflected with the opposite sign (right edge of the middle figure).
If the load resistance is greater than Z , the voltage jump is reflected with the same sign.

Signal reflections on incorrectly dimensioned load resistors can be described particularly easily if the voltage at the beginning of the cable changes very quickly and then remains constant. This voltage jump rushes through the cable at almost the speed of light and can be reflected at the end of the cable - depending on the reflection factor . The load voltage is then constant for the period 2 T and is calculated as with every superposition :

This leads to a stepped course, which is shown as the bottom picture and can be checked with an oscilloscope if the cables are long enough . The middle pictures show the location of the voltage jump (horizontal axis) as a function of time (vertical axis) as in a picture timetable .

The following assumptions apply to the adjacent images:

  • The voltage of a power supply with the internal resistance R source  = 0 Ω jumps  from zero to 12 V at time t = 0. For incoming voltage jumps, this source resistance acts like a short circuit that reverses the sign of the amplitude.
  • The line is lossless and has a characteristic impedance of Z  = 50 Ω.
  • The voltage jump takes the period T to the end of the line, where a load resistor R is connected.

Results for R  <  Z

The voltage jump is reflected at the end of the cable with the opposite sign and is weakened ( reflection factor ρ  <0) back to the source. If it reaches this, it is reflected  with the opposite sign and the same amplitude because of R source = 0 Ω . The voltage can  not change here because R source = 0 Ω.

It is noticeable that the load voltage U R only slowly reaches the end value U s , although no large capacity has to be charged (the capacitance per unit length of the cable is far from sufficient to explain this). The lower the value of the load resistance, the longer this period lasts, with R load  = 0 Ω it is of course infinite.

Results for R  >  Z

The voltage jump is reflected at the end of the cable with the same sign and runs  back to the source in a weakened manner (0 <  ρ <1).

It is noticeable that the load voltage U R exceeds the final value U s at periodic intervals, although there is no large inductance. If the cable is not under load (no load), U R can double the value of U s . So that connected circuits are not destroyed, they are often protected with varistors . The voltage curve at the load resistor is reminiscent of a damped oscillation around the setpoint U s . The higher the value of the load resistance, the longer this period lasts, with R load  = ∞ it is infinite.

special cases

The current through the switch doubles after the time 2 T from an initial 12 mA to 24 mA continuous current.
Up to time 2 T the current flows 12 mA and then drops to zero.

If you send a voltage jump in a cable whose end is open or short-circuited, the measurable voltage curves are simplified. The middle images show the location of the voltage jump (horizontal axis) as a function of time (vertical axis), the lower images show oscillograms. The following assumptions apply:

  • The voltage of a power supply with an internal resistance of W  =  Z  = 50 Ω jumps  from zero to 12 V at time t = 0. With this selection, incoming voltage jumps are absorbed without reflection.
  • The line is lossless and has a characteristic impedance of Z  = 50 Ω.
  • The voltage jump requires the period T to the end of the line.

Shorted end

The voltage at the beginning of the cable initially has half the value of the source voltage because of the voltage divider from W and Z. As soon as the jump, reflected in phase opposition, arrives at the beginning of the cable after the transit time 2 T , the voltage drops to zero and remains there. Since this time span can be selected to be very short, the process is also known as "electronic differentiation". With this circuit, a measuring signal that rises quickly and then falls again very slowly can be converted into a short needle pulse.

Open end

The voltage at the beginning of the cable initially has half the value of the source voltage because of the voltage divider from W and Z. As soon as the in-phase reflected jump arrives at the beginning of the cable after the transit time 2 T , the voltage doubles and remains at this level. Then the piece of cable is "charged".

The time reversal as a pulse generator is of technical importance : If the piece of cable “charged” with the voltage U is suddenly connected to a load resistor W  =  Z , the voltage U / 2 is applied for the (short) period of time 2 T. The precisely rectangular voltage curve can only be achieved with great difficulty with inductors. The very high efficiency is advantageous because no thermal energy is converted in the wave resistance of the line .

Applications

If there is an electronic circuit at the end of the cable, the load resistance is usually non-linear. For example, the inputs of CMOS circuits are very sensitive to static charges, which is why diodes are usually integrated against the two operating voltages in order to dissipate overvoltages. Then more complicated methods are required to calculate cable reflections.

Web links

credentials

  1. ↑ High Voltage Transient Analysis ( Memento of the original from June 29, 2012 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 132 kB) @1@ 2Template: Webachiv / IABot / www.elect.mrt.ac.lk
  2. ^ Dieter Suter: Electronics. (PDF; 3.8 MB) Archived from the original on July 4, 2017 ; accessed on May 1, 2017 .