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# Difference between RHC and LHC in receiving and transmitting antenna?

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#### Alan0354

##### Full Member level 4
How do you characterize an antenna in receiving mode? The book said a LHC antenna in transmitting mode is RHC in receiving mode. Also if the antenna is LHC in transmitting mode, it's transmission characteristic is defined as $\hat {E}_{(z,t)}=\frac{\hat {x}+\hat {y} j}{\sqrt{2}}$. But the same antenna is RHC in receiving mode and it's receiving characteristic is defined as $\hat {E}_{(z,t)}=\frac{\hat {x}-\hat {y} j}{\sqrt{2}}$?

Is it because the same antenna when characterized as LHC when transmitting in +z direction, when placed on the z axis as the receiving antenna, has to be characterized in -z direction and therefore is RHC antenna in receiving mode?

For RHC circular antenna in tx mode at the origin radiating in +z direction, the unit vector is $\hat {E}=\frac{\hat {x}+\hat{y}j}{\sqrt{2}}$.

1) What if the same RHC antenna radiating on the +z axis, but back TOWARDS the origin? The unit vector should be $\hat {E}=\frac{\hat {x}-\hat{y}j}{\sqrt{2}}$.

2) Also, the EM wave radiated by the RHC antenna from +z back towards the origin is represented by $\hat {E}=\frac{\hat {x}-\hat{y}j}{\sqrt{2}}$. also.

Am I correct?

In fact this is the example from Antenna Theory by Balanis 3rd edition p78 to 79. I don't agree with the book. It uses spherical coordinates and I disagree with the assertion that the antenna transmitting from a distance from the origin towards the origin is $\frac{\hat{\theta} +j\hat{\phi}}{\sqrt{2}$.

Also for RHC antenna in tx mode using as receiving antenna at the origin, I agree with the given equation. But that would give total loss in reception!!! I am confused, please help.

Thanks

How do you characterize an antenna in receiving mode? The book said a LHC antenna in transmitting mode is RHC in receiving mode. Also if the antenna is LHC in transmitting mode, it's transmission characteristic is defined as $\hat {E}_{(z,t)}=\frac{\hat {x}+\hat {y} j}{\sqrt{2}}$. But the same antenna is RHC in receiving mode and it's receiving characteristic is defined as $\hat {E}_{(z,t)}=\frac{\hat {x}-\hat {y} j}{\sqrt{2}}$?

Is it because the same antenna when characterized as LHC when transmitting in +z direction, when placed on the z axis as the receiving antenna, has to be characterized in -z direction and therefore is RHC antenna in receiving mode?

correct! this is because RH and LH are defined based on propagation direction.

- - - Updated - - -

For RHC circular antenna in tx mode at the origin radiating in +z direction, the unit vector is $\hat {E}=\frac{\hat {x}+\hat{y}j}{\sqrt{2}}$.

1) What if the same RHC antenna radiating on the +z axis, but back TOWARDS the origin? The unit vector should be $\hat {E}=\frac{\hat {x}-\hat{y}j}{\sqrt{2}}$.

2) Also, the EM wave radiated by the RHC antenna from +z back towards the origin is represented by $\hat {E}=\frac{\hat {x}-\hat{y}j}{\sqrt{2}}$. also.

Am I correct?

good thoughts!

1- radiation backward +z toward origin means -z!
2- yes.

Alan0354

### Alan0354

Points: 2

In fact this is the example from Antenna Theory by Balanis 3rd edition p78 to 79. I don't agree with the book. It uses spherical coordinates and I disagree with the assertion that the antenna transmitting from a distance from the origin towards the origin is $\frac{\hat{\theta} +j\hat{\phi}}{\sqrt{2}$.

Also for RHC antenna in tx mode using as receiving antenna at the origin, I agree with the given equation. But that would give total loss in reception!!! I am confused, please help.

Thanks

I read through the book over and over. I finally catch the part I missed. The book said $\hat{\rho}_a$ HAS to be defined as in transmitting mode. So if the RHC transmitting antenna is at origin outward, then the incident wave has the unit vector of $\hat{\rho}_a=\frac {\hat{x}+\hat{y}}{\sqrt{2}}$.

This together with the mistake the book make that the incident wave towards the origin, the unit vector of the wave should be $\hat{\rho}_w=\frac {\hat{x}-\hat{y}}{\sqrt{2}}$ due to the direction of propagation towards the origin. Then $\hat{\rho}_a \cdot \hat{\rho}_w=\left(\frac {\hat{x}+\hat{y}}{\sqrt{2}}\right)\cdot \left(\frac {\hat{x}-\hat{y}}{\sqrt{2}}\right)=1$.

Please confirm I got this one right. Thanks

Alan

PS: I know this is very tedious, but I really think this is important to clarify the polarity and the definition of the EM wave using a single coordination reference, not just RHC wave match with RHC antenna and hope it work out!!!

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