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Statement:
Consider two dipole antennas, oriented 90degrees apart [imagine the x-y plane, let "a" be the dipole oriented along the x-axis, and the "b" be the dipole oriented along the y-axis]. If "a" dipole radiates [tex]cos(\omega t)[/tex] and "b" dipole radiates [tex]sin(\omega t)[/tex], the field radiated by the two antennas will be circularly polarized:
[tex]\vec{E}(z, t) = E_{0}[cos(\omega t - \beta z)\hat{x} + sin(\omega t - \beta z)\hat{y}][/tex] (#1)
Side note: Very often, helical antennas are used to generate a circularly-polarized (CP) wave. The isolation between a left-handed CP wave and a right-handed CP wave can be significant. Also, a CP wave will change handedness upon reflection.
My thoughts:
I understand that [tex]E_0[/tex] is the magnitude of the sinusoid- and in this case it is circular thus both [tex]\hat{x}, \hat{y}[/tex] have the same amplitudes respectively. And since both [tex]sin(\omega t), cos(\omega t)[/tex] are perpendicular to one another, if one has a phase shift, the other will have the same phase shift [tex]\beta[/tex].
Relevant questions:
Is my thoughts above reasonable? What I would really like to know is why the electric field is a function of z also. What is the variable z, and how does it influence the electric field?
Also, can someone explain to me what is meant by
Thanks,
Jeffrey
Consider two dipole antennas, oriented 90degrees apart [imagine the x-y plane, let "a" be the dipole oriented along the x-axis, and the "b" be the dipole oriented along the y-axis]. If "a" dipole radiates [tex]cos(\omega t)[/tex] and "b" dipole radiates [tex]sin(\omega t)[/tex], the field radiated by the two antennas will be circularly polarized:
[tex]\vec{E}(z, t) = E_{0}[cos(\omega t - \beta z)\hat{x} + sin(\omega t - \beta z)\hat{y}][/tex] (#1)
Side note: Very often, helical antennas are used to generate a circularly-polarized (CP) wave. The isolation between a left-handed CP wave and a right-handed CP wave can be significant. Also, a CP wave will change handedness upon reflection.
My thoughts:
I understand that [tex]E_0[/tex] is the magnitude of the sinusoid- and in this case it is circular thus both [tex]\hat{x}, \hat{y}[/tex] have the same amplitudes respectively. And since both [tex]sin(\omega t), cos(\omega t)[/tex] are perpendicular to one another, if one has a phase shift, the other will have the same phase shift [tex]\beta[/tex].
Relevant questions:
Is my thoughts above reasonable? What I would really like to know is why the electric field is a function of z also. What is the variable z, and how does it influence the electric field?
Also, can someone explain to me what is meant by
Also, a CP wave will change handedness upon reflection?
Thanks,
Jeffrey