Dc load line

What is DC Load Line Analysis and Its Significance

In 1835 the Lloyd’s Register Group Limited introduced loading recommendations. The load line-markings are invented by Samuel Plimsoll (10 February 1824-3rd June 1898) in 1876. The main intention of the load line is to find the overloaded ships using the load line markers on the ship and these are found on side of the ship. In this article, we get to know the purpose of load lines and how they are used to find the loaded ships using the markers. So, this article discusses an overview of the dc load line analysis and its markings.

What is DC Load Line Analysis?

Definition: The DC (Direct Current) load line is a graph that has all possible volumes of output current (Ic) and output voltage (VCE) for a given amplifier. In the case of the amplifier, it has two inputs they are AC input and DC input. If we analyze the circuit for DC input then it is called a DC analysis. Similarly, if we have only AC input while analyzing then it is called AC analysis. If there are multiple sources available in the circuit you can treat one source at a time by using the superposition theorem.

Transistor DC Load Line

The transistor consists of the collector, emitter, and bias. The circuit diagram of the dc load line using a transistor is shown below. As shown in the figure, the DC battery V_BB is applied at the base and the collector terminals of the transistor. The voltage between collector and emitter is called V_CE and voltage between bias and emitter is called V_BE. To get the dc load line, we need to apply Kirchhoff’s Voltage Law to the output.

transistor-dc-load-line

By applying Kirchhoff’s Voltage Law to output will get

 V_CC-I_C*R_C-V_CE = 0

Hence we can write the above equation as

I_C*R_C = -V_CE +V_CC

Hence I_C = -1/ R_C * V_CE + V_CC

To draw the dc load line, we require a minimum of two points they are

Case 1: If we put I_C = 0, then will get V_CE = V_CC

Case 2: If we put V_CE = 0, then I_C becomes V_CC / R_C

By using the above two cases we can easily draw the dc load line for output characteristics. The dc load line is a graph of all values of I_C and V_CE. For common emitter configuration, the I_C and V_CE will be on output characteristics that’s why dc load line is drawn at output characteristics. If we plot using the above two cases, we will get the slope line and that line is called the dc load line.

The operating point ‘Q’ is defined as a point for a particular value of IC and the corresponding value of V_CE. We have to select the Q point exactly in the middle of the load line. When output characteristics intersect dc load line we can get different Q points.

Load Line Markings on Ships Side

A cargo ship is designed to carry different weights and volumes of cargo under the safe limit to avoid grounding and sinking of the vessel. The load line markers on a ship are shown in the below figure.

Load-line-markers

As shown in the above figure, the horizontal line is the deck line with a diameter 300mm and the round shape disc is the load line disc. From the center of the disc, the vertical lines are placed at a distance of 540mm. There are two types of load line markings they are standard load line-markings and timber load line-markings.

Standard Load Line Markings

The upper surfaces of the load line indicate the maximum depths to which the ships may be submerged in different seasons and circumstances. The letter ‘S’ in the load line marker is the Summer load line, it is the basic freeboard line at the same level as the plimsol line and other load lines are marked based on the summer freeboard line.

The letter ‘T’ in the load line marker is a tropical load line, it is 1/48th of the summer draft marked above the summer load line. The letter ‘W’ in load line marker is winter load, it is also a 1/48th of the summer draft marked below the summer load. The letter ‘WNA’ in the load line marker is winter North Atlantic load line is marked 50mm below the winter load line, it applies voyages in North Atlantic (above 36 degrees of latitude) during winter months.

The freshwater load line represented by a letter ‘F’, it is the summer fresh water line, the distance between summer and the freshwater line is the freshwater allowance. The Tropical freshwater load line is the freshwater load line in tropical and it is represented by TF, it is marked above the tropical line at an amount equal to freshwater allowance (FWA)

Timber Load Line Markings

The LS (Lumber Summer), LW (Lumber Winter), LT (Lumber Tropical), LWNA (Lumber Winter North Atlantic), LF (Lumber Fresh Water), and LTF (Lumber Fresh Water) are the timber load line-markings.

It is important for any ship to have a safe draft for safety and to avoid grounding. The draft can be measured vertically between the keel and the waterline of the ship. If the ship is loaded with more cargo, the draft will increase. The load line also helps in determining the freeboard of the ship which is the distance between the sheer and the waterline. Again if the draft increases, which means more volume of the cargo has been loaded leading to the decrease in the freeboard. If the freeboard is reduced more than the required limit, it may sink the vessel.

DC Load Line Analysis Significance

The significances of the DC load line are

By using the direct current load line concept, we can obtain the linear analysis of the circuit for non-linear elements such as diodes or transistors

The DC load line analysis main intention is to find the Quiescent Point (Q – point)

The Quiescent Point obtain by the dc load line at which the parameters voltage and current are equivalent to each other for both the parts of the circuit.

The signals amplified in dc load lines are less than the millivolts

The Quiescent Point obtained is essential while drawing the alternate current load lines

The dc voltage applied to the circuit varies when the resistance is constant