2.4.1. Voltage source with internal resistor

Voltage source with internal resistor
The general circuit diagram for such a voltage source is represented as a voltage source and a resistor in series.

Double line with voltage source and internal resistor

If no current is flowing, the so-called off-load voltage V₀ is measured between the outlets of the source.
If a current is flowing a voltage drop is found across this resistor R_i and only a reduced voltage is available at the external side.
The simulation allows to change the internal resistor R_i in order to study its influence on voltage and current on the double line.

(prepared simulation: 2-4-1-R-voltage-sourcs.xml)

Ergebnis:
The larger the resistance R I the smaller the voltage applied to the double line and the smaller the current and vice versa.

2.4.2. Double line with constant resistance on the lines

With all simulations used so far it was supposed that no losses are found on the lines. This is an idealisation that, for short lines, comes very close to reality. However, for longer lines losses are always present and can have a strong influence on the transmission of pulses.
The behaviour of such so-called lossy lines will be studied in the following. To do so it is assumed that both conductors of a double line provide a uniform resistance R_L for electric currents. This implies that per unit length a certain voltage is needed to drive a certain current through these conductors.
The simulation offers the possibility to study the influence of the line resistance on voltage and current along the line.

(prepared simulation: 2-4-2-const-R-on-line.xml)

Question:
Please observe voltage and current at the left entrance of the double line.
Why is the voltage at the entrance of the double line increased, when the loss-less lines are replaced by lines with resistance?
Answer

2.4.3. Double line with uniform conductivity between the lines (leakage)

The simulation program TL offers the possibility to simulate the influence of conductive material placed between the lines. As a result the two lines are electrically connected along their total length. The resistance of such a so-called leakage resistor can be changed.
In practical cases such leakage between conductors of a line is rather small and can often be neglected. In principle, however, it always exists.
The simulation allows to study its influence on the transmission of voltage and current.

(prepared simulation: 2-4-3-const-parallel-R.xml)

Question:
Please observe voltage and current at the left entrance of the double line. Why is this current increased, when the leakage resistor R(p) is applied in parallel to the load?
Answer

2.4.4. Single resistors on a double line

The simulation program TL offers the possibility to place on each line in the middle between load and source a resistor R_m of variable resistance. The result is a circuit with 3 resistors in series. The resitor R_m is changing the ratio U/I and therefore some part of an incoming wave front or puls will be partly reflected
Only after these reflections have faded away a dynamic equilibrium will be established, for which Ohm´s law is valid.

Double line with additional resistors in series with the terminating resistor
(prepared simulation: 2-4-4-single-resistor.xml)

Such transition processes will occur always when ever some conditions within the circuit are changed, either the voltage source is switched on or some resistors are changed.
Due to the high propagation velocity such processes are very short in time and are usually not observed.

2.4.5. Single resistor in parallel on a double line

As a rule the two conductors of a double line are isolated from each other and the resistance between them is practically infinite.
To study the behaviour of circuits with parallel resistors, however, the simulation program TL offers the possibility to simulate the influence of conductive material of a certain width and with variable resistance, placed between the two lines in the middle between source and load. Together with the load such a resistor forms a parallel circuit.
The simulation allows to study these reflection processes for various resistors.

Double line with an additional resistor in parallel with the terminating resistor (prepared simulation: 2-4-5-single-R-parallel.xml)

The parallel resistance causes a change of the ratio of U/I and therefore a wave front or pulse will be partly reflected.
Only after these reflections have faded away a dynamic equilibrium will be established, for which Ohm´s law is valid.

back to TL-tutorial (home page)