Antenna Radiation and propogation doubts

[TheArun]

I have a few doubts regarding antenna radiation and propogation. Kindly look into it and clarify.

Consider a Hertzian dipole antenna,

DOUBT # 1. Generally, when the power is mentioned for an antenna elements such as the power dissipated across radiation resistance(R_rad)

P radiated = (1/2)I²R_rad

Doubt:
1. Generally, Power equation is P = I²Resistance, but according to the above equation only 1/2 of the power across the radiation resistance is actually radiated. Is it a case of power lost and where?
2. Does the half term come from the equation of power across load allowing ac power i.e.,

P = V_rms * I_rms cos@

By taking the peak value of V and I and denoting V in terms of I it changes to, P = (1/2)I²R. If that is the case does that mean that,
a) Current, without mentioning explicitly is always considered to be an 'ac current peak value which is in phase with voltage'
and
b) If that is the case, does that also mean that Hertzian dipole or a current element that radiates as an antenna can only be made using a ac current and not dc current?

DOUBT#2: Consider a electric field having θ and φ component i.e.,
E = E_θ a_θ + E_φ a_φ
where,
E - electric field vector
Eθ - electric field component in θ direction and Eφ - Electric field compo in φ direction

So my doubt is what actually is this Eθ(or Eφ) which is a scalor along θ direction:
Is it a angle in θ direction ie say 30 deg in θ direction OR is it a distance?

 

[tech99]

I have a few doubts regarding antenna radiation and propogation. Kindly look into it and clarify.

Consider a Hertzian dipole antenna,

DOUBT # 1. Generally, when the power is mentioned for an antenna elements such as the power dissipated across radiation resistance(R_rad)

P radiated = (1/2)I²R_rad

Doubt:
1. Generally, Power equation is P = I²Resistance, but according to the above equation only 1/2 of the power across the radiation resistance is actually radiated. Is it a case of power lost and where?
2. Does the half term come from the equation of power across load allowing ac power i.e.,

P = V_rms * I_rms cos@

By taking the peak value of V and I and denoting V in terms of I it changes to, P = (1/2)I²R. If that is the case does that mean that,
a) Current, without mentioning explicitly is always considered to be an 'ac current peak value which is in phase with voltage'
and
b) If that is the case, does that also mean that Hertzian dipole or a current element that radiates as an antenna can only be made using a ac current and not dc current?

DOUBT#2: Consider a electric field having θ and φ component i.e.,
E = E_θ a_θ + E_φ a_φ
where,
E - electric field vector
Eθ - electric field component in θ direction and Eφ - Electric field compo in φ direction

So my doubt is what actually is this Eθ(or Eφ) which is a scalor along θ direction:
Is it a angle in θ direction ie say 30 deg in θ direction OR is it a distance?

Regarding Doubt 1, I think it is just confusion about peak and RMS.
Of course, up to half the power is wasted in the generator resistance, as with any system, but we normally specify transmitter power as that portion actually being delivered to the load. So all the transmitter output power is radiated.
For a receiving dipole, only half the incident power is delivered to the load, the remainder being re-radiated. This is also because of the source/load sharing issue.

 

[TheArun]

Regarding Doubt 1, I think it is just confusion about peak and RMS.
Of course, up to half the power is wasted in the generator resistance, as with any system, but we normally specify transmitter power as that portion actually being delivered to the load. So all the transmitter output power is radiated.
For a receiving dipole, only half the incident power is delivered to the load, the remainder being re-radiated. This is also because of the source/load sharing issue.

Thanks for the reply.But you have not cleared my doubt. So, what is the current in the above equations? Is it peak value or rms value?

 

[tech99]

Thanks for the reply.But you have not cleared my doubt. So, what is the current in the above equations? Is it peak value or rms value?

It is the convention that AC currents and voltages are RMS values unless stated otherwise. So your formula should use RMS current and should not include the factor 1/2.

 

[TheArun]

It seems no one is here to clear this doubt.
Thanks tech99 for replying. The equation I wrote here is from a textbook, so may be they meant peak value.
But no one is saying about, is it possible to make with DC current or my 2nd doubt

 

[Jeff Rosenbury]

Radiation resistance is a fudge factor. It directly represents the power radiated into space through special relativity. As such it should not include the ½ (as tech99 stated.). If it does in your textbook, it is either a mistake, or their definition of radiation resistance includes some other losses. (Resistive losses due to power matching in the antenna make some sense, but who can say?) For a more generally used equation, check Wikipedia.

Your second doubt should be defined by the conventions the book is using. Variables mean what they are defined to mean. Usually θ and φ are defined as angles (but this is not a requirement). So E_θ a_θ sounds like the E field in the θ direction times some number/function a that's associated with θ somehow. (What or where the field is isn't clear.) But without more information, it's hard to tell. Given the earlier ½ I don't even want to guess at the meaning.

Changing magnetic fields make currents. Charges will also travel through resistances to make currents. But unless there's a way to regenerate these, you will not get a DC current. DC generators move the rotor through a constant rate of changing field. Batteries produce new charge at a constant rate.

I'm not sure what you want to do with your E field, but it should be possible to get a DC current through some combination of these techniques. (It might not be easy though.)

 

[TheArun]

What I meant by Eθ aθ is just according to normal convention. Eθ is the component of electric field in θ direction(as in spherical coordinates) and aθ is the unit vector (it is 'a caps θ' , I cudn't find a proper symbol for that)
So my doubt is what actually is this Eθ(or Eφ) which is a scalor along θ direction:
Is it a angle in θ direction ie say 30 deg in θ direction OR is it a distance?
If it was in rectangular coods, Eθ is a distance in aθ direction...what about this coods?