# How is the amplitude of an output signal of a binary input determined using a constellation pattern?

I understand using the pattern to find the output line single phase but how is the amplitude determined?

But how is the amplitude determined?

By the length of the line from the origin to each constellation point: -

The above image has equal amplitudes for all four binary values hence they sit on the circumference of a circle.

The one below has 8 binary values and the amplitude of the inner four is smaller than the outer four.

• Is this true as well for a binary signal? Commented Jan 23, 2020 at 16:48
• It usually is but needn’t be theoretically. BPSK (binary phase shift keying) is a good example of two points having equal amplitude but a phase angle of 180 degrees between the two signals. Commented Jan 23, 2020 at 16:50
• So first image is 1v. 5v, 0v range second image would be 1v, 0.75v ,0.5v 0v range? Commented Jan 23, 2020 at 16:59
• I don’t know how you arrived at those numbers frankly. In the 1st diagram, all amplitudes are the same because all four binary vales are represented on one circle having a constant radius. Commented Jan 23, 2020 at 17:04
• If you are wondering how each constellation point is ascribed a binary value then that is completely arbitrary. The example binary values in my pictures are purely examples and need not be like that. Commented Jan 23, 2020 at 17:06