Block Diagram Simplification Part-1 By ECE Tech Notes

💡 Tips to solve block diagram:

• Blocks is series gets multiplied.
• Blocks in parallel gets added.
• Shifting the take-off point to left side = multiplication of blocks.
• Shifting the take-off point to right side = division of blocks.
• Shifting the summing point to left side = division of blocks.
• Shifting the summing point to right side = multiplication of blocks.
• After shifting the summing point, the existing summing point gets eliminated.

Example Problems:

1. Find the transfer function of the block diagram given below.

In order to find the transfer function, we have to reduce or simplify the given block diagram.

Shift the take-off point of H1 to the left side.

After shifting, the the BD get's reduced as shown below.

After solving the F/b loop, the block reduces.

Now, G3G4 & G5 are in parallel and get's added as shown below.

Since all the blocks are in series, so all blocks get's multiplied as shown below.

After solving the F/b loop, the BD get's reduced as shown below.

Finally, the TF of a BD is given by,

2. Find the transfer function of the block diagram given below.

In order to find the transfer function, we have to reduce or simplify the given block diagram.

Shift the summing point of 'H3' to LHS and take off point to RHS.

After shifting, the G1G2 and G3G4 are in series as shown below.

Now, G1G2H1 and G3G4H2 forms a feedback loop.

After solving the two F/b loops, the BD get's reduced as shown below.

The two blocks in series get's multiplied as shown below.

After solving the F/b loop, the blocks reduces as shown below.

Finally the TF of a BD is,

3. Find the transfer function of the block diagram given below.

Shift the take off point H2 to the right side as shown below.

After shifting, the BD gets reduces as shown below.

Now the BD has two F/b loop and one F/w loop, and the reduced BD is shown below.

Since all the blocks are in series, so the all blocks will get multiplied as shown below.

Now the block has unity gain F/b loop, after reducing it we get,

Finally, the TF of a BD is given by,

4. Find the transfer function of the block diagram given below.

Now, shift the take off point 'H1' to left side as shown below. 

After shifting, the BD gets reduced. And we know that, shifting the take off point to the left side = multiplication of blocks with take off point as shown below.

After solving, the block gets reduced as shown below.

Since all the blocks are in series, the blocks gets reduced as shown below.

Finally, the TF of a BD is given by,