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Calculation of line of sight system gain

1

$begingroup$

I'm trying to calculate the overall gain of the transmitter-receiver system for a line-of-sight wireless transmission with the following properties:

• A carrier frequency of 0.5GHz


• A distance between the transmitter and receiver antennas of 2Km


• A parabolic antenna in the transmitter with a face area of 0.8m²


• An infinitesimal dipole in the receiver

---

From what I can understand/determine the equation for calculating gain is:

G = 4π*effective area/carrier wavelength/carrier wavelength OR

G = 4π*carrier frequency²*effective area/speed of light²

---

My question is how to calculate the overall gain of the system. Is it as simple as calculating the gain of the transmitter and receiver separately and then adding them together?

signal-analysis

share|improve this question

asked 2 hours ago

Lily HaynesLily Haynes

61

New contributor

Lily Haynes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

1

$begingroup$

I'm trying to calculate the overall gain of the transmitter-receiver system for a line-of-sight wireless transmission with the following properties:

• A carrier frequency of 0.5GHz


• A distance between the transmitter and receiver antennas of 2Km


• A parabolic antenna in the transmitter with a face area of 0.8m²


• An infinitesimal dipole in the receiver

---

From what I can understand/determine the equation for calculating gain is:

G = 4π*effective area/carrier wavelength/carrier wavelength OR

G = 4π*carrier frequency²*effective area/speed of light²

---

My question is how to calculate the overall gain of the system. Is it as simple as calculating the gain of the transmitter and receiver separately and then adding them together?

signal-analysis

share|improve this question

asked 2 hours ago

Lily HaynesLily Haynes

61

New contributor

Lily Haynes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

I'm trying to calculate the overall gain of the transmitter-receiver system for a line-of-sight wireless transmission with the following properties:

• A carrier frequency of 0.5GHz


• A distance between the transmitter and receiver antennas of 2Km


• A parabolic antenna in the transmitter with a face area of 0.8m²


• An infinitesimal dipole in the receiver

---

From what I can understand/determine the equation for calculating gain is:

G = 4π*effective area/carrier wavelength/carrier wavelength OR

G = 4π*carrier frequency²*effective area/speed of light²

---

My question is how to calculate the overall gain of the system. Is it as simple as calculating the gain of the transmitter and receiver separately and then adding them together?

signal-analysis

share|improve this question

asked 2 hours ago

Lily HaynesLily Haynes

61

New contributor

Lily Haynes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

asked 2 hours ago

Lily HaynesLily Haynes

61

New contributor

Lily Haynes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 2 hours ago

Lily HaynesLily Haynes

61

New contributor

Lily Haynes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Lily HaynesLily Haynes

61

New contributor

Lily Haynes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Lily HaynesLily Haynes

61

1 Answer
1

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1

$begingroup$

You need to multiply the antenna gains, not add them. Specifically, if the free-space loss (attenuation) is $L_FS$, the transmitter antenna has gain $G_T$, and the receiver antenna has gain $G_R$, then the total system loss $L$ is $$ L = fracL_FSG_T G_R. $$ The system gain $G$ is $$G = frac1L = G_FSG _T G_R, $$ where $G_FS$ is the free-space gain.

Of course, if you're doing the calculation in decibels, then the antenna gains are added: $$ G_dB = G_FS,dB + G_T,dB + G_R,dB. $$

share|improve this answer

answered 1 hour ago

MBazMBaz

9,08041733

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you that's really helpful but I'm a bit confused as to how to calculate the free-space gain that you talked about. I understand how to calculate the free-space loss, but I can't seem to find any information about free-space gain?
  $endgroup$
  – Lily Haynes
  57 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I focused on the gain since that is what you mention in your question. The gain is just the reciprocal of the loss: $G = 1/L$. If all you need is the loss, you can use the first formula in my answer; in decibels, it'd be $L_dB = L_FS,dB - G_T,dB - G_R,dB$.
  $endgroup$
  – MBaz
  19 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Perfect, I understand now, thank you for your help!
  $endgroup$
  – Lily Haynes
  17 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You're welcome; glad to be of help!
  $endgroup$
  – MBaz
  16 mins ago
  

  
  
  
  

add a comment | 

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1

$begingroup$

You need to multiply the antenna gains, not add them. Specifically, if the free-space loss (attenuation) is $L_FS$, the transmitter antenna has gain $G_T$, and the receiver antenna has gain $G_R$, then the total system loss $L$ is $$ L = fracL_FSG_T G_R. $$ The system gain $G$ is $$G = frac1L = G_FSG _T G_R, $$ where $G_FS$ is the free-space gain.

Of course, if you're doing the calculation in decibels, then the antenna gains are added: $$ G_dB = G_FS,dB + G_T,dB + G_R,dB. $$

share|improve this answer

answered 1 hour ago

MBazMBaz

9,08041733

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you that's really helpful but I'm a bit confused as to how to calculate the free-space gain that you talked about. I understand how to calculate the free-space loss, but I can't seem to find any information about free-space gain?
  $endgroup$
  – Lily Haynes
  57 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I focused on the gain since that is what you mention in your question. The gain is just the reciprocal of the loss: $G = 1/L$. If all you need is the loss, you can use the first formula in my answer; in decibels, it'd be $L_dB = L_FS,dB - G_T,dB - G_R,dB$.
  $endgroup$
  – MBaz
  19 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Perfect, I understand now, thank you for your help!
  $endgroup$
  – Lily Haynes
  17 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You're welcome; glad to be of help!
  $endgroup$
  – MBaz
  16 mins ago
  

  
  
  
  

add a comment | 

1

$begingroup$

You need to multiply the antenna gains, not add them. Specifically, if the free-space loss (attenuation) is $L_FS$, the transmitter antenna has gain $G_T$, and the receiver antenna has gain $G_R$, then the total system loss $L$ is $$ L = fracL_FSG_T G_R. $$ The system gain $G$ is $$G = frac1L = G_FSG _T G_R, $$ where $G_FS$ is the free-space gain.

Of course, if you're doing the calculation in decibels, then the antenna gains are added: $$ G_dB = G_FS,dB + G_T,dB + G_R,dB. $$

share|improve this answer

answered 1 hour ago

MBazMBaz

9,08041733

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you that's really helpful but I'm a bit confused as to how to calculate the free-space gain that you talked about. I understand how to calculate the free-space loss, but I can't seem to find any information about free-space gain?
  $endgroup$
  – Lily Haynes
  57 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I focused on the gain since that is what you mention in your question. The gain is just the reciprocal of the loss: $G = 1/L$. If all you need is the loss, you can use the first formula in my answer; in decibels, it'd be $L_dB = L_FS,dB - G_T,dB - G_R,dB$.
  $endgroup$
  – MBaz
  19 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Perfect, I understand now, thank you for your help!
  $endgroup$
  – Lily Haynes
  17 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You're welcome; glad to be of help!
  $endgroup$
  – MBaz
  16 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

You need to multiply the antenna gains, not add them. Specifically, if the free-space loss (attenuation) is $L_FS$, the transmitter antenna has gain $G_T$, and the receiver antenna has gain $G_R$, then the total system loss $L$ is $$ L = fracL_FSG_T G_R. $$ The system gain $G$ is $$G = frac1L = G_FSG _T G_R, $$ where $G_FS$ is the free-space gain.

Of course, if you're doing the calculation in decibels, then the antenna gains are added: $$ G_dB = G_FS,dB + G_T,dB + G_R,dB. $$

share|improve this answer

answered 1 hour ago

MBazMBaz

9,08041733

$endgroup$

share|improve this answer

answered 1 hour ago

MBazMBaz

9,08041733

answered 1 hour ago

MBazMBaz

9,08041733

answered 1 hour ago

MBazMBaz

9,08041733