---
title: Antenna
tags:
- SAR
- physics
- basic
date: 2023-06-30
---

# Theorem you need know

* [🧷Resonant circuit](physics/electromagnetism/resonant_circuit.md)

# What is antenna

A usually metallic device for radiating or receiving radio waves

## A simple model representing antenna

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230404163712.png)

* $R_L$ 损耗电阻 - 介质与结构导致的损耗
* $R_r$ 辐射电阻 - 与天线产生的辐射的能量关系密切
* $X_A$ 电抗 - 描述天线近场电磁能转换的现象 (一般情况下$X_A$ = 0)

> [!warning] 
> 天线还有一个很重要的损耗来源，**mismatch loss**, 天线跟前端的阻抗不匹配，导致能量打不进天线，这点可以通过设计和材质来解决 

# Types of antennas

## Wire antennas

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230404165239.png)

## Aperture antennas

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230410105310.png)

## Microstrip antennas

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230410105548.png)

## Array antennas

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230410111719.png)

> [!hint] 
> 天线的目的简单来说，就是为了将能量尽可能辐射出去，同时按照你希望的方向和区间辐射。

## Reflector antennas & Lens antennas

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230410112252.png)


# Radiation mechanism

## Ideal antenna

Radiate all the power delivered to it from the transmitter in a desired direction or directions.

## How is radiation accomplished?

* How are EM fields generated by the source?
* How are EM fields contained and guided within the transmission line & antenna?
* How are EM fields finally detached from the antenna to form a free-space wave?

### How are EM fields generated by the source?
 
![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230410113039.png)

* $q_v$电荷密度，$C/m^3$
* $v_Z$电荷移动速度，$m/s$
* $J_Z$电流密度，$A/m^2$
$$
A/m^2 = C/m^3 * m/s = \frac{C}{m^2 * s}
$$

导线由PEC所做时，或者高频情况，电流变成面电流
* $J_S$变成面电流密度，$A/m^2$
* $q_S$也变成面电荷密度，$C/m^2$

但wire非常thin，当然面最终被认为为线

$$
I_Z = q_l v_Z
$$
我们用thin wire case来讨论

对这个式子做时间微分
$$
\frac{dI_z}{dt} = q_l\frac{v_Z}{dt}=q_l a_z
$$
$$
l\frac{dI_Z}{dt}=lq_la_Z=Qa_z
$$
> [!hint] 
> To create radiation, there must be **a time-varying current** or **an acceleration (or deceleration) of charge** 
> 
> -> The wire must be curved, bent, discontinuous, terminated, or truncated

###  How are EM fields contained and guided within the transmission line & antenna?

![](electrical_electronics/RF/algrothim/SAR/attachments/Pasted%20image%2020230411105457.png)

radiation要考虑两个方面，一方面激发电场那边提供的电子的加速，另一方面时end部分的pause造成的电子的减速，这两边会有最主要的辐射；

如果加速和减速之间的距离很短，形成一个pulse，会发出一个很宽频的信号；

如果加减速达到间歇运动状态，会发出一个单频的辐射

> [!hint] 
> 用水波去理解辐射
> 
> 在池塘里要产生水波，你可以丟一颗石头
> 
> Source可以产生pulse或者弦波，引起电磁振荡，induce电荷做加减速，产生时变电流，在导线里产生导波，也就是在传输线中引导的电磁波，电磁波最后会走到天线端，被辐射出去；
> 
> pulse就像你丢了一颗石头下去，弦波就像你按照周期去丢
 
> [!hint] 
> 根据[Maxwell's equations](physics/electromagnetism/maxwells_equation.md)
> 
> 当电磁波在导线中存在的时候，它是需要时变的电流或者说是加减速的电荷来support。在传输线里，需要source才能有场；
> 
> 但是在解[Maxwell's equations](physics/electromagnetism/maxwells_equation.md)的时候，是有一组homogeneous的解，这组解指的是，你不需要source的存在的场，这个场指的是free-space wave；
> 
> 所以，天线本质上就是一个interface，将导线内需要source的场，变成不需要source的场，也就是free-space wave

### How are EM fields finally detached from the antenna to form a free-space wave?

# Radar key Parameters



# Reference

* [知乎 - 天线与电波传播基础知识](https://zhuanlan.zhihu.com/p/497482699)
* [天线 in wiki](https://zh.wikipedia.org/wiki/%E5%A4%A9%E7%BA%BF)
* [⭐⭐⭐陈士元 - 天线原理与基本参数](https://www.youtube.com/watch?v=JsVGW3z81wc&list=PLQdXflQNtKfLaGnvPLW_XVal-RaHxFN5j&index=1)
* [天线8个核心参数解析 - 知乎 (zhihu.com)](https://zhuanlan.zhihu.com/p/375911768)