## What is Bewley's Lattice Diagram?

Consider a resistive load R_{L} connected to a generator G having resistance R_{g} through a transmission line of characteristic impedance Z_{c} as shown in the future below.

If a voltage or current wave is sent to the load by the generator then, the wave reflects back to the generator after reaching the load R_{L}. Again due to the presence of resistance, R_{g} at the generator side, the wave reflects back to the load. Hence, the wave suffers from repeated reflections and to monitor these reflections, Bewley's lattice diagram is drawn, which is also called the zig-zag diagram.

In the lattice diagram, two axes are provided, a horizontal axis representing the distance along with the system and a vertical axis. showing time. The passage of surges is represented by the lines who's slopes provide the time equal to the distance travelled. The reflected and transmitted waves can be achieved at any point of change impedance by multiplying the magnitudes of incidence waves with their relevant refraction and reflection coefficients.

Lattice diagrams can also be drawn for current, only when the reflection coefficient of current is negative of the reflection coefficient of voltage. For the system shown in the above figure, where a generator unit with internal resistance R_{g} is switched on a line without attenuation having a characteristic or surge impedance Z_{C}, with load resistance R_{L} at its receiving end.

#### The reflection coefficient at the receiving end is given by, The reflection coefficient at the sending end is given by,

Let T be the time interval of surge from one end of the line to the other. Now, as soon as the generator unit is switched ON, a step voltage surge of infinite length travels down the line towards the receiving end. This is represented by a line sloping (left to right) as shown in the figure below.

When the surge reaches the load end in time T seconds, a surge of amplitude Î±_{R} is generated in the reflection process. This surge is then travelling towards the generator end and reaches the end in time 2T seconds. It is represented by a line sloping (right to left). The reflection at the generator end originates an outward surge of strength Î±_{R} Î±_{s}. This process continues endlessly and some of its steps are shown in the figure above.

From Bewley's Lattice diagram, it is observed that, at the receiving end, the increment of voltage at each reflection is the sum of the incident and reflected waves. After initiate reflections, the reflection voltage V_{R} becomes,