习题六
1．光接收机中有哪些噪声
答：热噪声、散粒噪声和自发辐射噪声。
2．RZ码和NRZ码有什么特点
答：NRZ（非归零码）：编码1对应有光脉冲，且持续时间为整个比特周期，0对应无光脉冲。RZ（归零码）：编码1对应有光脉冲，且持续时间为整个比特周期的一半，0对应无光脉冲。NRZ码的优点是占据频宽窄，只是RZ码的一半；缺点是当出现长连“1”或“0”时，光脉冲没有交替变换，接收时对比特时钟的提取是不利的。RZ码解决了长连“1”的问题，但长连“0”的问题没解决。
3．通信中常用的线路码型有哪些
答：扰码、mBnB码、插入码和多电平码。
4．光源的外调制都有哪些类型内调制和外调制各有什么优缺点
答：光源的外调制类型有：电折射调制、电吸收MQW调制、M-Z型调制。内调制器简单且廉价，这种调制会引起输出光载波的频率啁啾；外调制器可以有更高的速率工作，并且有较小的信号畸变。
5．假定接收机工作于1550nm，带宽为3GHz，前置放大器噪声系数为4dB，接收机负载为![](https://wkrtcs.bdimg.com/rtcs/image?w=89&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"89","h":"23","c":"e2c7452a968d4f93be5b9a15b043dcb3.png"})
解：接收机工作于1550nm，则电离系数比为![](https://wkrtcs.bdimg.com/rtcs/image?w=69&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"69","h":"23","c":"6fbfef57fd275d64af4cdc67545be28e.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=350&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"350","h":"46","c":"5301b7eba24e1eca3fa6c260280a138e.png"})
热噪声电流方差为
![](https://wkrtcs.bdimg.com/rtcs/image?w=134&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"134","h":"49","c":"e6b60078ea9d7f0eea5f2c575f3d1bf4.png"})
接收机灵敏度为
![](https://wkrtcs.bdimg.com/rtcs/image?w=239&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"239","h":"69","c":"1e5f55f93af74fcca4d7477033a12fca.png"})
6．在考虑热噪声和散粒噪声的情况下，设APD的![](https://wkrtcs.bdimg.com/rtcs/image?w=111&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"111","h":"31","c":"4f371a5b1cc653cadaf4ba41f7e7d276.png"})
解：光接收机输出端的信噪比定义为：
![](https://wkrtcs.bdimg.com/rtcs/image?w=56&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"56","h":"20","c":"89de8d8f62bfad52e0f387eb73e70c90.png"})
光检测器的噪声功率表示为
![](https://wkrtcs.bdimg.com/rtcs/image?w=232&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"232","h":"32","c":"11f18b08fec9435692033fade7b6ede0.png"})
其中![](https://wkrtcs.bdimg.com/rtcs/image?w=70&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"70","h":"23","c":"70b96ec4a2d46ee634dab7952fa27a91.png"})
假设放大器的输入阻抗远大于负载电阻![](https://wkrtcs.bdimg.com/rtcs/image?w=25&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"25","h":"23","c":"c9265d932e54ef2d16900350eb67d785.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=139&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"139","h":"49","c":"a51dac511b26817d3f7f02232cd18bea.png"})
其中![](https://wkrtcs.bdimg.com/rtcs/image?w=23&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"23","h":"23","c":"3c55419967d78bff97d6a021132c947d.png"})
放大器输入端的信号功率为![](https://wkrtcs.bdimg.com/rtcs/image?w=73&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"73","h":"37","c":"9072e31b90bd28e60022a80678eb0f6e.png"})
得到放大器输入端的信噪比为
![](https://wkrtcs.bdimg.com/rtcs/image?w=337&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"337","h":"84","c":"023e461f999dbc445288c763f7c6ebd4.png"})
设APD的
![](https://wkrtcs.bdimg.com/rtcs/image?w=295&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"295","h":"84","c":"229b0644ba138f3ef38482a863c2d976.png"})
要使APD接收机的SNR最大，可以求出一个最佳的![](https://wkrtcs.bdimg.com/rtcs/image?w=28&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"28","h":"23","c":"ad3a9cfb5827fa3c2e2e607611be4fef.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=196&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"196","h":"57","c":"190d7efcf8426973590ed015860d8670.png"})
7．证明：对于OOK直接检测接收机，其误码率公式为
![](https://wkrtcs.bdimg.com/rtcs/image?w=155&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"155","h":"50","c":"62244c77e29c63c79db3e87f8e462320.png"})
证明： “0”码被误判为“1”码和“1”码被误判为“0”码的几率一样，不妨就以“1”码被误判为“0”码为例来计算误码率。“1”码被误判为“0”码的概率为
![](https://wkrtcs.bdimg.com/rtcs/image?w=227&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"227","h":"50","c":"53b916fe306d5e4a7fe6d946cc7146e0.png"})
当“0”码被误判为“1”码和“1”码被误判为“0”码的几率一样时，阈值电流为
![](https://wkrtcs.bdimg.com/rtcs/image?w=130&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"130","h":"49","c":"b8329afea849f19c3a638f5aeaed9b58.png"})
代入上式得到
10．推导具有光放大器的光接收机的误码率![](https://wkrtcs.bdimg.com/rtcs/image?w=226&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"226","h":"69","c":"3691b5b725ecbf6726ebaa6e5d2192b5.png"})
证明：当输入为“1”码时，有光输入，光检测器输出的光生电流（均值电流）与入射光功率成正比
![](https://wkrtcs.bdimg.com/rtcs/image?w=72&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"72","h":"23","c":"2ef0a24404008e1aa90a709b23647e13.png"})
在接收机中，信号与噪声的差动噪声电流方差（“1”码时光生电流方差）为
![](https://wkrtcs.bdimg.com/rtcs/image?w=202&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"202","h":"31","c":"d1a1840fe4eae155ed63657972bd1943.png"})
“0”码时的光生电流![](https://wkrtcs.bdimg.com/rtcs/image?w=45&md5sum=d1a2ae8945a1099c03afd932b3ea2667&sign=301a99bbb4&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=485&ipr={"t":"img","w":"45","h":"23","c":"4f189caec6aa8ab569377801577c7b48.png"})
得到
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