# Is an antenna resonant at the frequency of lowest impedance?

I understand that an antenna is resonant at the frequency where the capacitive and inductive reactance cancel out to 0. Only the resistive impedance remains at resonance.

Does this mean that the impedance is lowest at the frequency where only the resistive impedance remains? Can we find the resonant frequency of an antenna by looking for the lowest point on it's impedance curve?

• Welcome to ham.stackexchange.com! Nov 18 '19 at 17:26
• Impedance is a complex number, and there exists no total ordering on the complex numbers. So precisely what do you mean by "lowest impedance"? Nov 18 '19 at 18:45
• I think it's obvious that he means the frequency at which the resistive part of the impedance is lowest, Nov 19 '19 at 0:19
• Yes Phil, I incorrectly thought you can somehow sum the reactive and resistive components of impedance. I now know that's not the case. Nov 19 '19 at 1:36
• @Andrew is it obvious? Maybe he means the argument of the impedance. Nov 19 '19 at 15:09

Marcin, as you have alluded to, an antenna is resonant when there is no reactance present in the impedance seen at the feed point for the frequency you are using. There is no reactance because at resonance the antenna voltage and current are in phase, not because the inductive and capacitive reactances cancel out. When the antenna is not resonant, the voltage and current are not in phase which results in the impedance containing some reactance.

Assuming you are not changing the antenna or it's feed point and you are changing the frequency, the frequency at which the impedance has the lowest resistance (ignoring if there is any reactance present) does not however always match up with resonance.

The value of the resistive or real part of the impedance does not determine whether or not the antenna is resonant. At resonance there is no reactance, not least resistance.

• Ok, I understand now. I mistakenly thought that a complex impedance can be stated as a single number. Now I know it can only be defined as 2 numbers. Nov 19 '19 at 1:32
• If you want to learn about complex numbers see en.wikipedia.org/wiki/Complex_number. Nov 19 '19 at 1:39
• Thank's that's helpful. Nov 19 '19 at 1:41
• Also, you don't want the antenna to have the lowest resistance or impedance. You want it to have the impedance that matches the radio and feed line -- which is usually 50 ohms (or 50+0i ohms complex). the best match to the radio is where the magnitude of the difference of 50+0i and the impedance of the antenna is smallest. This is where you get the best power transfer -- but it may still not be where it is resonant! Frequently in amateur radio, this is considered where it is resonant however. Nov 25 '19 at 2:16

A point to remember here is: A transmit antenna does not need to be self-resonant at the operating frequency to be a very efficient radiator of e-m energy.

A matching network at the antenna input terminals may be used to match the impedance of that antenna (including its non-zero reactive term) to the impedance of the transmission line connected there.

Such antenna systems are commonly used by medium-wave AM broadcast stations, and may radiate >95% of the r-f energy at the input of their matching network(s).

• a good point but your response doesn't answer the question at all. Nov 18 '19 at 11:26
• Understood, but the reality of my response may affect the importance of seeking an answer to the original question, and of value to the OP (and others). Nov 18 '19 at 13:39
• A followup question (and one I pondered myself) is: why would the resistance change with frequency? The answer to that is provided by Phil here (ham.stackexchange.com/questions/2435/…) Nov 19 '19 at 14:48