matching 2nd harmonics frequency

Do anyone can help me on how to match the network at the 2nd harmonics frequency? IF look at the smith chart from S1,1 how can we determine and match the network based on it? Any characteristics that must be meet to match the 2nd harmonics network? let say the fundamental frequency is 5 GHz.

Actually I think you are looking to reject the second harmonic at the input of the amplifier. In this case to do not degrade the Gain of the amplifier doing the input match only for 2nd harmonic, probably the best is to place a notch filter at the input of the amplifier.
The notch could be part of the input matching network, to do not degrade the S11 at fundamental.

Actually I am doing the frequency multiplier. So I want to have maximum 2nd harmonics output power. Therefore, the gain for fundamental is need to degrade. Normally, we match the series open stub based on Smith chart to do for the fundamentals . Any idea to do for 2nd harmonics?

If is about a frequency multiplier this is a different story.
In this case you have to use a LPF at the input and a BPF at the output as in the picture below.
The input matching network shall have reactive termination at harmonic frequencies which ensure optimum conversion gain and isolation from the output.
The output network ensures matching at second-harmonic frequency and terminates the fundamental frequency and the higher-order harmonics with reactive terminations, in order to reject the fundamental and higher-order harmonics, and ensure isolation from the input.

So, from the graph i paste below is it the graph match at 4 GHz at 2nd harmonics frequency?

simply use standard matching with tranmission lines and stub

khouly

The span of your picture is only up to 2.1GHz, so I don?t know how looks at 4GHz.