【大学生电子竞赛题目分析】——2019年全国赛G题《双路语音同传的无线收发系统》
<div class='showpostmsg'><p style="text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:黑体">一、任务 </span></span></span></span></span></p><p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">设计制作一个双路语音同传的无线收发系统，实现在一个信道上同时传输两路话音信号。系统的示意图如图所示。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:黑体">二、要求 </span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="115%">1. </span><span style="115%"><span style="font-family:宋体">基本要求</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">1</span><span style="115%"><span style="font-family:宋体">）制作一套</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">无线收发系统。其中，</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">信号的载波频率设定为</span></span><span lang="EN-US" style="115%">48.5MHz</span><span style="115%"><span style="font-family:宋体">，相对误差的绝对值不大于</span></span><span lang="EN-US" style="115%">1</span><span style="115%"><span style="font-family:宋体">‰；峰值频偏不大于</span></span><span lang="EN-US" style="115%">25kHz</span><span style="115%"><span style="font-family:宋体">；天线长度不大于</span></span><span lang="EN-US" style="115%">0.5m</span><span style="115%"><span style="font-family:宋体">。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">2</span><span style="115%"><span style="font-family:宋体">）通过</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">无线收发系统任意传输一路语音信号</span></span><span lang="EN-US" style="115%">A</span><span style="115%"><span style="font-family:宋体">或者</span></span><span lang="EN-US" style="115%">B</span><span style="115%"><span style="font-family:宋体">，语音信号的带宽不大于</span></span><span lang="EN-US" style="115%">3400Hz</span><span style="115%"><span style="font-family:宋体">。要求无线通信距离不小于</span></span><span lang="EN-US" style="115%">2m</span><span style="115%"><span style="font-family:宋体">，解调输出的语音信号波形无明显失真。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">3</span><span style="115%"><span style="font-family:宋体">）通过</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">无线收发系统同时传输双路语音信号</span></span><span lang="EN-US" style="115%">A</span><span style="115%"><span style="font-family:宋体">和</span></span><span lang="EN-US" style="115%">B</span><span style="115%"><span style="font-family:宋体">。要求无线通信距离不小于</span></span><span lang="EN-US" style="115%">2m</span><span style="115%"><span style="font-family:宋体">，解调输出的双路语音信号波形无明显失真。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="115%">2. </span><span style="115%"><span style="font-family:宋体">发挥部分</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">1</span><span style="115%"><span style="font-family:宋体">）要求设计制作的发射电路中</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">信号的载波频率能通过一个电压信号</span></span><i><span lang="EN-US" style="115%">v<sub>C</sub> </span></i><span lang="EN-US" style="115%">(<i>t</i>)</span><span style="115%"><span style="font-family:宋体">进行调节，用来模拟无线通信中载波频率漂移的情况。电压信号</span></span><i><span lang="EN-US" style="115%">v<sub>C</sub> </span></i><span lang="EN-US" style="115%">(<i>t</i>)</span><span style="115%"><span style="font-family:宋体">单位电压调节载波频率产生的频率漂移量，由参赛者自行设计。</span></span> </span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">2</span><span style="115%"><span style="font-family:宋体">）在保证系统能正确进行双路语音无线传输的前提下，通过</span></span><i><span lang="EN-US" style="115%">v<sub>C</sub> </span></i><span lang="EN-US" style="115%">(<i>t</i>)</span><span style="115%"><span style="font-family:宋体">信号调节</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">信号的载波频率产生不小于</span></span><span lang="EN-US" style="115%">300 kHz</span><span style="115%"><span style="font-family:宋体">的漂移，要求调节时间</span></span><span lang="EN-US" style="115%">τ </span><span style="115%"><span style="font-family:宋体">不超过</span></span><span lang="EN-US" style="115%">5s</span><span style="115%"><span style="font-family:宋体">（秒）。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">3</span><span style="115%"><span style="font-family:宋体">）在保证系统能正确进行双路语音无线传输的前提下，通过</span></span><i><span lang="EN-US" style="115%">v<sub>C</sub> </span></i><span lang="EN-US" style="115%">(<i>t</i>)</span><span style="115%"><span style="font-family:宋体">信号调节</span></span><span lang="EN-US" style="115%"> FM </span><span style="115%"><span style="font-family:宋体">信号的载波频率，按照下图所示进行漂移，要求</span></span><span lang="EN-US" style="115%"> FM</span><span style="115%"><span style="font-family:宋体">信号的载波频率漂移范围</span></span><span lang="EN-US" style="115%">Δ<i>f </i><sub>0</sub></span><span style="115%"><span style="font-family:宋体">越大越好。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">4</span><span style="115%"><span style="font-family:宋体">）其他。</span></span></span></span></span></span></p>
<p style="text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:黑体">三、说明 </span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">1</span><span style="115%"><span style="font-family:宋体">）系统输入的语音信号，可以由标准的信号源产生；解调的语音信号输出应留有测试接口，以便示波器观测。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">2</span><span style="115%"><span style="font-family:宋体">）制作的</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">发射电路应在发射天线端引出测试端口，以便测试。</span></span> </span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="115%"><span style="font-family:宋体">（</span></span><span lang="EN-US" style="115%">3</span><span style="115%"><span style="font-family:宋体">）控制</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">信号的载波频率漂移的外加电压信号</span></span><i><span lang="EN-US" style="115%">v<sub>C</sub> </span></i><span lang="EN-US" style="115%">(<i>t</i>)</span><span style="115%"><span style="font-family:宋体">通过标准信号源外部输入。外加的</span></span><i><span lang="EN-US" style="115%">v<sub>C</sub> </span></i><span lang="EN-US" style="115%">(<i>t</i>)</span><span style="115%"><span style="font-family:宋体">信号为零时，</span></span><span lang="EN-US" style="115%">FM</span><span style="115%"><span style="font-family:宋体">信号的载波频率漂移对应为零。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
</div><script> var loginstr = '<div class="locked">查看精华帖全部内容，请<a href="javascript:;" style="color:#e60000" class="loginf">登录</a>或者<a href="https://bbs.eeworld.com.cn/member.php?mod=register_eeworld.php&action=wechat" style="color:#e60000" target="_blank">注册</a></div>';
if(parseInt(discuz_uid)==0){
(function($){
var postHeight = getTextHeight(400);
$(".showpostmsg").html($(".showpostmsg").html());
$(".showpostmsg").after(loginstr);
$(".showpostmsg").css({height:postHeight,overflow:"hidden"});
})(jQuery);
}
</script><script type="text/javascript">(function(d,c){var a=d.createElement("script"),m=d.getElementsByTagName("script"),eewurl="//counter.eeworld.com.cn/pv/count/";a.src=eewurl+c;m.parentNode.insertBefore(a,m)})(document,523)</script> <p align="left" style="margin-top:8px; text-align:left"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="line-height:115%"><span style="font-family:黑体">题目分析与方案设计</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制与解调是一个基本通信电路，在大学高频电路课程中都有，所以总体方案不是问题。本题的设计难点在于下列几点：</span></span><span lang="EN-US" style="color:#444444">1</span><span style="font-family:宋体"><span style="color:#444444">、</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">信号发生器，要求</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">载频有</span></span><span lang="EN-US" style="line-height:115%">1</span><span style="line-height:115%"><span style="font-family:宋体">‰的频率精度，同时要求有</span></span><span lang="EN-US" style="line-height:115%">300kHz</span><span style="line-height:115%"><span style="font-family:宋体">以上的载频漂移。</span></span><span lang="EN-US" style="line-height:115%">2</span><span style="font-family:宋体"><span style="color:#444444">、双路语音同传。</span></span><span lang="EN-US" style="color:#444444">3</span><span style="font-family:宋体"><span style="color:#444444">、在载频漂移情况下的接收。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">以前在本论坛曾经发过一个帖子，对这个题目做过一些讨论。这次仔细分析了题目，</span></span></span></span></span></span><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">下面依次分析这几个问题，做出一些具体的定量分析，也修正了原先帖子中的一些不足。。</span></span></span></span></span></span></p>
<p style="margin-top:8px; text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">1</span><span style="font-family:宋体"><span style="color:#444444">、</span></span><b><span lang="EN-US" style="color:#444444">FM</span></b><b><span style="font-family:宋体"><span style="color:#444444">信号发生</span></span></b></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">常见的</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">信号可以由以下几种方法产生：压控振荡器直接调频、压控晶体振荡器直接调频、锁相环调频、</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">产生调频信号。下面分析这些方法的特点、适用范围以及在本题目应用中的要点。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">a) </span><span style="font-family:宋体"><span style="color:#444444">压控振荡器（</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">）直接调频。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">可以是</span></span><span lang="EN-US" style="color:#444444">RC</span><span style="font-family:宋体"><span style="color:#444444">振荡器，也可以是基于变容二极管的</span></span><span lang="EN-US" style="color:#444444">LC</span><span style="font-family:宋体"><span style="color:#444444">振荡器。这个方法是最简单的</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制器，容易获得足够的频偏，也容易做到在外加电压下的载频漂移。问题是振荡器的频率精度和稳定度很难保证，要实现题目的</span></span><span lang="EN-US" style="line-height:115%">1</span><span style="line-height:115%"><span style="font-family:宋体">‰的频率精度很难，即使在电路设计、元件选择与安装调试等多方面非常注意，也只能做到短期稳定</span></span><span style="font-family:宋体"><span style="color:#444444">。所以这个方案通常只用于演示以及玩具级的应用。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">b) </span><span style="font-family:宋体"><span style="color:#444444">压控晶体振荡器（</span></span><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">）直接调频。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">是一种商品级的器件，它通过变容二极管改变石英晶体振荡器的振荡频率，因此频率精度和稳定度极好。</span></span><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">的主要问题是相对频偏很小，通常只有</span></span><span lang="EN-US" style="color:#444444">±</span><span lang="EN-US" style="color:#444444">100ppm~</span><span lang="EN-US" style="color:#444444">±</span><span lang="EN-US" style="color:#444444">200ppm</span><span style="font-family:宋体"><span style="color:#444444">。用</span></span><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">实现调频应该将</span></span><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">的最大频偏控制在其允许的范围之内，然后通过倍频</span></span><span lang="EN-US" style="color:#444444">-</span><span style="font-family:宋体"><span style="color:#444444">混频的方法，逐步将频偏扩大。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">本题要求的载频为</span></span><span lang="EN-US" style="color:#444444">48.5MHz</span><span style="font-family:宋体"><span style="color:#444444">，最大频偏为</span></span><span lang="EN-US" style="color:#444444">25kHz+150kHz</span><span style="font-family:宋体"><span style="color:#444444">（其中</span></span><span lang="EN-US" style="color:#444444">25kHz</span><span style="font-family:宋体"><span style="color:#444444">是调制信号的最大频偏，</span></span><span lang="EN-US" style="color:#444444">150kHz</span><span style="font-family:宋体"><span style="color:#444444">是准直流漂移的最大频偏），相对频偏大约是</span></span><span lang="EN-US" style="color:#444444">3600ppm</span><span style="font-family:宋体"><span style="color:#444444">，远大于</span></span><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">的允许频偏，所以要扩大频偏，具体做法如下：</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">先对一个</span>50MHz<span style="font-family:宋体">的</span>VCXO<span style="font-family:宋体">进行调频，控制最大频偏为</span>1kHz+6kHz<span style="font-family:宋体">（其中</span>1kHz<span style="font-family:宋体">为调制频偏，</span>6kHz<span style="font-family:宋体">为漂移频偏），此时的相对频偏只有</span>140ppm<span style="font-family:宋体">左右，在</span>VCXO<span style="font-family:宋体">的可控频偏范围内。然后用锁相环对此信号</span>5<span style="font-family:宋体">倍频，得到中心频率为</span>250MHz<span style="font-family:宋体">、频偏为</span>5kHz+30kHz<span style="font-family:宋体">的</span>FM<span style="font-family:宋体">信号。再将此</span>FM<span style="font-family:宋体">信号与一个</span>200MHz<span style="font-family:宋体">的信号混频，取其下边频，则其中心频率降到</span>50MHz<span style="font-family:宋体">，但是频偏不变。再重复</span>5<span style="font-family:宋体">倍频过程，得到中心频率为</span>250MHz<span style="font-family:宋体">、频偏为</span>25kHz+150kHz<span style="font-family:宋体">的</span>FM<span style="font-family:宋体">信号。再与</span>201.5MHz<span style="font-family:宋体">的信号混频，最终得到题目要求的中心频率</span>48.5MHz<span style="font-family:宋体">、频偏</span>25kHz+300kHz<span style="font-family:宋体">的</span>FM<span style="font-family:宋体">信号。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">从上面的例子也可以看到，</span><span lang="EN-US" style="color:#444444">VCXO</span><span style="font-family:宋体"><span style="color:#444444">直接调频</span></span><span style="font-family:宋体">对于相对频偏较小的</span>FM<span style="font-family:宋体">信号调制还是很好用的，所以它常常应用于数字信号的调制（例如</span>FSK<span style="font-family:宋体">）。但是对于相对频偏较大的</span>FM<span style="font-family:宋体">信号，可能要反复多次倍频</span>-<span style="font-family:宋体">混频的过程，电路变得比较繁复。就如对于本题来说，由于要模拟载频漂移导致相对频偏较大，所以不是一个最好的方案。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">c) DDS</span><span style="font-family:宋体"><span style="color:#444444">直接产生</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">信号。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">由于</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">的参考频率基于石英晶体，所以这种方法的频率精度和稳定度极好，也能得到足够的频偏并实现模拟载频漂移。从理论上说改变</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">的输出频率是一个非连续的步进变化过程，但由于</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">可以做到极小的频率步进改变，实际上可认为是一种准连续的调制过程，所以它也能实现</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">但</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">芯片的</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制是通过微处理器不断改变芯片内部的相位增量实现的，所以它比较适合于有规律的频率变化过程，例如信号发生器之类。本题的调制信号为语音，其频率幅度均随机变化，用</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">产生</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制时要先用微处理器对输入的语音信号进行</span></span><span lang="EN-US" style="color:#444444">ADC</span><span style="font-family:宋体"><span style="color:#444444">采样，然后根据采样结果去改变</span></span><span lang="EN-US" style="color:#444444">DDS</span><span style="font-family:宋体"><span style="color:#444444">的相位增量，实际结构比较复杂，并非最佳方案。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">d) </span><span style="font-family:宋体"><span style="color:#444444">锁相环调频。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">锁相环调频的参考频率是由石英晶体提供的，所以这个方法有极好的频率精度和稳定性，也能够提供足够的频偏，对于本题来说可能是一个最好的方案。下面针对本题的具体要求作一些具体分析。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="line-height:115%"><span style="font-family:宋体">下图是锁相环</span></span><span lang="EN-US" style="line-height:115%">FM</span><span style="line-height:115%"><span style="font-family:宋体">调制电路的基本结构。</span></span><span style="font-family:宋体">在这个电路中，锁相环的参考频率来自石英晶体，其</span><span style="line-height:115%"><span style="font-family:宋体">稳定性极高，可以认为它是固定不变的。但是</span></span>VCO<span style="font-family:宋体">输出的</span>FM<span style="font-family:宋体">信号频率</span><span style="line-height:115%"><span style="font-family:宋体">在不断变化，所以</span></span><span style="font-family:宋体">在大部分时间内，鉴相器的两个输入频率是不同的。换言之，锁相</span>FM<span style="font-family:宋体">电路中的锁相环大部分时间都工作在失锁状态。当采用鉴相</span>-<span style="font-family:宋体">鉴频器（</span>PFD<span style="font-family:宋体">）鉴相时，仅在</span>FM<span style="font-family:宋体">信号频率接近载频附近的几个周期内</span>PFD<span style="font-family:宋体">工作在鉴相状态，输出交替的正负脉冲，而在其余的大部分时间内</span>PFD<span style="font-family:宋体">都工作在鉴频状态，其输出是高电平或低电平，所以</span>PFD<span style="font-family:宋体">的输出近似为一个频率与调制信号频率相同的方波。环路滤波器的目的是取出这个近似方波的平均值作为</span>VCO<span style="font-family:宋体">的中心控制电压，从而保证</span>FM<span style="font-family:宋体">信号的中心频率始终与参考频率同步。从这个意义上看，此时的锁相环似乎称为“锁频环”更加恰当一些。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">下图示意了鉴相器</span>PFD<span style="font-family:宋体">输出与环路滤波器</span>LF<span style="font-family:宋体">输出之间的关系。在调制信号的一个周期中，</span>FM<span style="font-family:宋体">信号的频率围绕载波频率作周期变化，</span>PFD<span style="font-family:宋体">的输出为一个近似方波。由于环路滤波器的</span>RC<span style="font-family:宋体">时间常数通常总是远大于调制信号周期，所以</span>LF<span style="font-family:宋体">输出电压近似为一个三角波，其平均值</span><i>V<sub>H</sub></i>/2<span style="font-family:宋体">对应的是</span>FM<span style="font-family:宋体">信号的载波频率，而</span>LF<span style="font-family:宋体">输出电压波动就对应着</span>FM<span style="font-family:宋体">信号中载波频率的波动。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> <span style="font-size:10.5pt"><span style="font-family:宋体">将</span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">LF</span></span><span style="font-size:10.5pt"><span style="font-family:宋体">输出电压近似为三角波后，可写出它</span></span><span style="font-size:10.5pt"><span style="font-family:宋体">偏离平均电压的最大值</span></span><span style="font-size:10.5pt"><span style="font-family:宋体">为</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> <span style="font-size:10.5pt"><span style="font-family:宋体">此值对应着输出</span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">FM</span></span><span style="font-size:10.5pt"><span style="font-family:宋体">信号中载波频率波动的最大值（注意是载波的波动，不是调制引起的最大频偏）。由于</span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">V<sub>H</sub></span></span></i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">/2</span></span><span style="font-size:10.5pt"><span style="font-family:宋体">对应着载波频率，所以载波频率波动的最大相对误差就是</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">上式可以作为锁相环</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">电路的一个基本设计公式。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">回到本题目，</span></span><span style="line-height:115%"><span style="font-family:宋体">要求</span></span><span style="font-family:宋体"><span style="color:#444444">载波频率相对误差不大于</span></span><span lang="EN-US" style="line-height:115%">1</span><span style="line-height:115%"><span style="font-family:宋体">‰，代入上述公式，就是要求</span></span><span lang="EN-US" style="line-height:115%"> (<i>R</i><sub>1</sub>+<i>R</i><sub>2</sub>)<i>C </i>>1000<i>T</i>/4</span><span style="line-height:115%"><span style="font-family:宋体">。题目规定调制信号为语音信号，通常语音信号的频率范围为</span></span><span lang="EN-US" style="line-height:115%">300Hz~3400Hz</span><span style="line-height:115%"><span style="font-family:宋体">，所以调制信号的最大周期为</span></span><i><span lang="EN-US" style="line-height:115%">T</span></i><span lang="EN-US" style="line-height:115%">=3.3ms</span><span style="line-height:115%"><span style="font-family:宋体">。将此值代入，得到此电路中环路滤波器设计的一个条件是</span></span><span lang="EN-US" style="line-height:115%"> (<i>R</i><sub>1</sub>+<i>R</i><sub>2</sub>)<i>C </i>>0.83s</span><span style="line-height:115%"><span style="font-family:宋体">，在设计时可取</span></span><span lang="EN-US" style="line-height:115%">1s</span><span style="line-height:115%"><span style="font-family:宋体">。这是一个很大的时间常数，为了保证不会因负载电阻影响而降低其值，通常需要在环路滤波器的输出端接入一个具有高输入阻抗的缓冲器，例如运放构成的跟随器。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="font-family:宋体">这个锁相环中另一个基本公式是阻尼因子</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">其中</span><i>K<sub>d</sub></i><span style="font-family:宋体">是</span>PFD<span style="font-family:宋体">的增益，</span><i>K<sub>o</sub></i><span style="font-family:宋体">是</span>VCO<span style="font-family:宋体">的增益，</span><i>K<sub>f</sub></i><span style="font-family:宋体">是环路滤波器的增益（包括后续的电压缓冲器以及加法器的权重系数），</span><i>N</i><span style="font-family:宋体">是反馈回路的分频系数。</span><span style="line-height:115%"><span style="font-family:宋体">考虑锁相环的稳定性，通常要求</span></span><i><span lang="EN-US" style="line-height:115%">ζ</span></i><span style="line-height:115%"><span style="font-family:宋体">在</span></span><span lang="EN-US" style="line-height:115%">0.7~1</span><span style="line-height:115%"><span style="font-family:宋体">。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="font-family:宋体">根据上述两个基本公式就可以完成环路滤波器的设计。</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">题目中还有一个</span></span><span style="line-height:115%"><span style="font-family:宋体">模拟无线通信中载波</span></span><span style="font-family:宋体"><span style="color:#444444">频率漂移的要求，其指标概括如下：</span></span><span style="line-height:115%"><span style="font-family:宋体">通过一个标准信号源外部输入一个电压信号</span></span><i><span lang="EN-US" style="line-height:115%">v<sub>C</sub> </span></i><span lang="EN-US" style="line-height:115%">(<i>t</i>)</span><span style="line-height:115%"><span style="font-family:宋体">使得载波频率发生变化（漂移），</span></span><span style="font-family:宋体"><span style="color:#444444">最大变化量为</span></span><span lang="EN-US" style="color:#444444">±150kHz</span><span style="font-family:宋体"><span style="color:#444444">。</span></span><span style="line-height:115%"><span style="font-family:宋体">外加的</span></span><i><span lang="EN-US" style="line-height:115%">v<sub>C</sub> </span></i><span lang="EN-US" style="line-height:115%">(<i>t</i>)</span><span style="line-height:115%"><span style="font-family:宋体">信号为零时，</span></span><span lang="EN-US" style="line-height:115%">FM</span><span style="line-height:115%"><span style="font-family:宋体">信号的载波频率漂移对应为零。</span></span><span style="font-family:宋体"><span style="color:#444444">下面分析实现这个要求的电路及其注意点。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">将漂移电压与音频信号电压叠加后作为</span>VCO<span style="font-family:宋体">的调制电压，就可以实现输出频率的漂移，电路结构如下图。其中</span><i>R</i><sub>3</sub>~<i>R</i><sub>5</sub><span style="font-family:宋体">构成电阻加法器，三个电阻的阻值决定了三个信号的权重。调制信号是一个交流信号，采用电容耦合可以保证它不会影响输入</span>VCO<span style="font-family:宋体">的电压平均值，也就是不会影响载波频率。而漂移电压是一个直流信号，所以必须采用直流耦合。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> <span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">由于</span>PFD<span style="font-family:宋体">输出的平均电压为</span><i>V<sub>H</sub></i>/2<span style="font-family:宋体">对应的是</span>FM<span style="font-family:宋体">信号的载波频率</span>48.5MHz<span style="font-family:宋体">，而按照题目的要求，外加的漂移电压是正负变化的，当它为</span>0<span style="font-family:宋体">时</span>FM<span style="font-family:宋体">信号的载波频率为</span>48.5MHz<span style="font-family:宋体">，所以应该将外加的漂移电压的零电位平移到</span><i>V<sub>H</sub></i>/2<span style="font-family:宋体">，上面电路中以一个叠加的偏置电压表示这个电压的平移，在实际电路的调试中可以微调这个偏置电压，使得外加的漂移电压为</span>0<span style="font-family:宋体">时，锁相环正常进入锁定状态，</span>VCO<span style="font-family:宋体">的控制电压接近</span><i>V<sub>H</sub></i>/2<span style="font-family:宋体">。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">下面讨论外加的漂移电压不等于</span>0<span style="font-family:宋体">的状态。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">假设输入一个较大的漂移电压，则</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">在此阶跃输入下其输出频率（载频）发生阶跃变化。由于锁相环的负反馈作用，</span></span><span lang="EN-US" style="color:#444444">PFD</span><span style="font-family:宋体"><span style="color:#444444">会输出一个与漂移电压反相的电平（</span></span><i><span lang="EN-US" style="color:#444444">V<sub>H</sub></span></i><span style="font-family:宋体"><span style="color:#444444">或者</span></span><span lang="EN-US" style="color:#444444">0</span><span style="font-family:宋体"><span style="color:#444444">），这个电平经过环路滤波器后将输出一个按指数规律变化的电压，此电压将部分抵消输入的漂移电压，使得实际的载频漂移量减小。因此</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">的输出频率在开始的阶跃变化后，将随着环路滤波器的输出变化而逐渐向初始频率靠拢。但是由于环路滤波器的最终输出受到电源电压的限制，经过</span></span><span lang="EN-US" style="color:#444444">3</span><span lang="EN-US" style="color:#444444">τ</span><span lang="EN-US" style="color:#444444">~5</span><span lang="EN-US" style="color:#444444">τ</span><span style="font-family:宋体"><span style="color:#444444">以后将趋于其极限，所以只要合理安排两个输入电阻（</span></span><i><span lang="EN-US" style="color:#444444">R</span></i><sub><span lang="EN-US" style="color:#444444">3</span></sub><span style="font-family:宋体"><span style="color:#444444">与</span></span><i><span lang="EN-US" style="color:#444444">R</span></i><sub><span lang="EN-US" style="color:#444444">5</span></sub><span style="font-family:宋体"><span style="color:#444444">）的权重，就可以保证</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">最后达到预定的输出频率。下图就是上述频率变化的示意。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="line-height:115%"><span style="font-family:宋体">题目中有一个要求：“通过</span></span><i><span lang="EN-US" style="line-height:115%">v<sub>C</sub> </span></i><span lang="EN-US" style="line-height:115%">(<i>t</i>)</span><span style="line-height:115%"><span style="font-family:宋体">信号调节</span></span><span lang="EN-US" style="line-height:115%">FM</span><span style="line-height:115%"><span style="font-family:宋体">信号的载波频率产生不小于</span></span><span lang="EN-US" style="line-height:115%">300 kHz</span><span style="line-height:115%"><span style="font-family:宋体">的漂移，要求调节时间</span></span><span lang="EN-US" style="line-height:115%">τ </span><span style="line-height:115%"><span style="font-family:宋体">不超过</span></span><span lang="EN-US" style="line-height:115%">5</span><span style="line-height:115%"><span style="font-family:宋体">秒”。这个描述有些含糊，但按照字面的理解就是指上述输入阶跃变化的漂移电压的情况。而根据上述分析，若环路滤波器的时间常数</span></span><i><span lang="EN-US" style="line-height:115%">τ</span></i><span lang="EN-US" style="line-height:115%">=(<i>R</i><sub>1</sub>+<i>R</i><sub>2</sub>)<i>C</i>=1s</span><span style="line-height:115%"><span style="font-family:宋体">，那么经过</span></span><span lang="EN-US" style="line-height:115%">5s</span><span style="line-height:115%"><span style="font-family:宋体">即</span></span><span lang="EN-US" style="line-height:115%">5</span><span lang="EN-US" style="color:#444444">τ</span><span style="font-family:宋体"><span style="color:#444444">以后其输出已经接近极限，电路已经稳定，可以满足题目的要求。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">从上述讨论也可以看到，在较大的漂移电压作用下，环路滤波器最后处于输出饱和状态（输出一直维持在高电平或一直维持在低电平），实际上锁相环已经处于开环状态，整个电路蜕变为</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">直接调频电路。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">但是在输入的漂移电压很小的一个范围内，由于锁相环的负反馈，</span></span><span lang="EN-US" style="color:#444444">LF</span><span style="font-family:宋体"><span style="color:#444444">的输出电压与输入的漂移电压抵消，锁相环仍然处于锁定状态，其输出的中心频率保持不变（频率牵引现象）。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">题目发挥部分第</span></span><span lang="EN-US" style="color:#444444">3</span><span style="font-family:宋体"><span style="color:#444444">条要求输出载频按照三角波变化。若输入的偏移电压信号为一个三角波时，由于上述锁相环的频率牵引作用，锁相环的输出在中心频率</span></span><span lang="EN-US" style="color:#444444">48.5MHz</span><span style="font-family:宋体"><span style="color:#444444">附近会出现一段频率不变的锁定过程，当外加偏移达到锁相环无法锁定时，输出频率将跳变到某个频率后开始变化，其频率</span></span><span lang="EN-US" style="color:#444444">-</span><span style="font-family:宋体"><span style="color:#444444">时间曲线有点类似</span></span><span lang="EN-US" style="color:#444444">B</span><span style="font-family:宋体"><span style="color:#444444">类推挽放大器的交越失真。不过由于题目没有这方面的要求，所以似乎不用加以改进。</span></span></span></span></span></span></p>
<p style="margin-top:8px; text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">2</span><span style="font-family:宋体"><span style="color:#444444">、<b>双路语音同传问题</b></span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">由于双路语音的频谱重叠，所以不能将它们简单地用加法器叠加，那样两路信号将无法区分。正确的做法是先将其中一路信号的频谱移动，使得两路信号的频谱不再重叠，然后将两路信号叠加。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">具体做法可以参考调频立体声广播：将某路音频信号</span></span><span lang="EN-US" style="color:#444444">B</span><span style="font-family:宋体"><span style="color:#444444">对一个副载频进行</span></span><span lang="EN-US" style="color:#444444">AM</span><span style="font-family:宋体"><span style="color:#444444">调制（调频立体声广播采用的是抑制载频的</span></span><span lang="EN-US" style="color:#444444">AM</span><span style="font-family:宋体"><span style="color:#444444">调制，这里为了以后解调方便可以采用普通</span></span><span lang="EN-US" style="color:#444444">AM</span><span style="font-family:宋体"><span style="color:#444444">调制）为信号</span></span><span lang="EN-US" style="color:#444444">B</span><span lang="EN-US" style="color:#444444">'</span><span style="font-family:宋体"><span style="color:#444444">，然后将它与另一路音频信号</span></span><span lang="EN-US" style="color:#444444">A</span><span style="font-family:宋体"><span style="color:#444444">叠加成为复合音频信号。上述频谱关系如下：</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">为了解调时滤波方便，信号</span></span><span lang="EN-US" style="color:#444444">B</span><span lang="EN-US" style="color:#444444">'</span><span style="font-family:宋体"><span style="color:#444444">与信号</span></span><span lang="EN-US" style="color:#444444">A</span><span style="font-family:宋体"><span style="color:#444444">之间应该保留一定的频率间隔</span></span><span style="font-family:宋体"><span style="color:#444444">。已知信号</span></span><span lang="EN-US" style="color:#444444">A</span><span style="font-family:宋体"><span style="color:#444444">与</span></span><span lang="EN-US" style="color:#444444">B</span><span style="font-family:宋体"><span style="color:#444444">的带宽均为</span></span><span lang="EN-US" style="color:#444444">3400Hz</span><span style="font-family:宋体"><span style="color:#444444">，</span></span><span style="font-family:宋体"><span style="color:#444444">因此副载频应该大于</span></span><span lang="EN-US" style="color:#444444">3400Hz</span><span style="font-family:宋体"><span style="color:#444444">的两倍，例如</span></span><span style="font-family:宋体"><span style="color:#444444">可以取副载频为</span></span><span lang="EN-US" style="color:#444444">9kHz</span><span style="font-family:宋体"><span style="color:#444444">，此时复合信号的最高频率为</span></span><span lang="EN-US" style="color:#444444">9000+3400=12.4kHz</span><span style="font-family:宋体"><span style="color:#444444">。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">发送端用上述复合音频信号对主载波进行</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制（调制电路已在前面介绍了），就可以得到双路同传的已调波。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">接收端对接收到的</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">信号进行下变频、中放等一系列处理（在后面有具体分析）后，进行</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">解调（鉴频）得到复合音频信号。然后用一个低通滤波器可以直接得到信号</span></span><span lang="EN-US" style="color:#444444">A</span><span style="font-family:宋体"><span style="color:#444444">，用一个带通滤波器可以得到被副载波调制后的信号</span></span><span lang="EN-US" style="color:#444444">B</span><span lang="EN-US" style="color:#444444">'</span><span style="font-family:宋体"><span style="color:#444444">，再将这个信号进行</span></span><span lang="EN-US" style="color:#444444">AM</span><span style="font-family:宋体"><span style="color:#444444">解调（检波）就可以得到信号</span></span><span lang="EN-US" style="color:#444444">B</span><span style="font-family:宋体"><span style="color:#444444">。下图就是针对本题的解调电路结构。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">其中的鉴频器可以是锁相鉴频器、斜率鉴频器等，其中以</span></span><span lang="EN-US" style="color:#444444">LC</span><span style="font-family:宋体"><span style="color:#444444">谐振回路构成的斜率鉴频器最容易制作与调试。检波器则以二极管大信号检波电路最为简单方便。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">下图是</span></span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">LC</span></span></span><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">谐振回路斜率鉴频器。</span></span></span><span style="font-size:10.5pt"><span style="font-family:宋体">电路的核心是</span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">L</span></span></i><span style="font-size:10.5pt"><span style="font-family:宋体">、</span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">C</span></span></i><sub><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">1</span></span></sub><span style="font-size:10.5pt"><span style="font-family:宋体">与</span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">C</span></span></i><sub><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif">2</span></span></sub><span style="font-size:10.5pt"><span style="font-family:宋体">构成的谐振回路。该电路具有两个谐振点：并联谐振频率</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> <span style="font-size:10.5pt"><span style="font-family:宋体">串联谐振频率</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> <span style="font-size:10.5pt"><span style="font-family:宋体">两个谐振频率位于中频频率两侧对称的位置。</span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">当输入</span>FM<span style="font-family:宋体">已调信号的频率高于中频时，由于趋向于并联谐振频率，所以</span><i>v<sub>p</sub></i><span style="font-family:宋体">幅度加大；当已调信号的频率低于中频时，趋向于串联谐振频率，</span><i>v<sub>s</sub></i><span style="font-family:宋体">幅度加大。</span><i>v<sub>p</sub></i><span style="font-family:宋体">与</span><i>v<sub>s</sub></i><span style="font-family:宋体">通过二极管检波取出其直流分量，由最后一个运放构成的减法器相减并滤除其中的中频成分后，就成为</span>FM<span style="font-family:宋体">信号的解调输出。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">此解调器的输出电压与输入信号频率的关系曲线是</span>LC<span style="font-family:宋体">回路在两个谐振频率的谐振曲线的反相叠加（并联减去串联），根据其形状被称为</span>S<span style="font-family:宋体">曲线。中间线性较好的部分是有效鉴频范围。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">电感的</span>Q<span style="font-family:宋体">值影响</span>S<span style="font-family:宋体">曲线的斜率，也就是鉴频电路的鉴频增益。电阻</span>R4<span style="font-family:宋体">影响两个谐振峰的比值，也就是</span>S<span style="font-family:宋体">曲线的对称性，调试时应该通过微调此电阻获得良好的鉴频特性。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="margin-top:8px; text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">3</span><span style="font-family:宋体"><span style="color:#444444">、</span></span><b><span style="font-family:宋体">载频漂移下的接收问题</span></b></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">这个难点在于接收端的处理，涉及接收机的选择性以及鉴频电路的灵敏度。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">接收端通常采用超外差式接收电路。这种电路的选择性主要取决于中频放大器的选频特性，在满足调制信号的频谱要求前提下，中频放大器的选频特性越好则接收机的噪声越低。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">另外，</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">解调常采用斜率鉴频器或锁相鉴频器等电路，这些电路都有一个共性，就是解调器的工作频率范围越窄则解调灵敏度就越高。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">常规的超外差电路的本振频率是固定的，当输入信号的频率漂移后，送到中频放大器的信号频率也会漂移。考虑到输入频率可能的漂移，中频放大器选频网络的带宽以及鉴频器的工作频率范围通常设计得略大于信号带宽。本题规定</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">调制的最大频偏小于</span></span><span lang="EN-US" style="color:#444444">25kHz</span><span style="font-family:宋体"><span style="color:#444444">，所以在一般情况下中频放大器的带宽与鉴频器的工作频率范围只要略大于</span></span><span lang="EN-US" style="color:#444444">50kHz</span><span style="font-family:宋体"><span style="color:#444444">即可正常接收。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">但是在这个题目中，频率漂移的范围非常大。按照题目要求，载频漂移大于</span></span><span lang="EN-US" style="color:#444444">300kHz</span><span style="font-family:宋体"><span style="color:#444444">（</span></span><span lang="EN-US" style="color:#444444">±</span><span lang="EN-US" style="color:#444444">150kHz</span><span style="font-family:宋体"><span style="color:#444444">），如果采用固定的本振频率，则中频放大器要有大于</span></span><span lang="EN-US" style="color:#444444">300kHz</span><span style="font-family:宋体"><span style="color:#444444">的通带带宽，鉴频器的工作频率范围也必须大于</span></span><span lang="EN-US" style="color:#444444">300kHz</span><span style="font-family:宋体"><span style="color:#444444">。但是这就与上述正常的</span></span><span lang="EN-US" style="color:#444444">50kHz</span><span style="font-family:宋体"><span style="color:#444444">带宽构成了巨大的矛盾。如此大的中频带宽与鉴频频率范围将导致输出信号的信噪比极差。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">解决此问题的关键是设法保证中频频率不变。如果能够使得本振频率随着输入信号频率的漂移变化而变化，那么整个中频放大器和鉴频器等就都可以按照常规的超外差电路进行设计。这种电路通常被称为自动频率控制（</span></span><span lang="EN-US" style="color:#444444">AFC</span><span style="font-family:宋体"><span style="color:#444444">）电路。具体的电路结构见下图。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">此电路用一个压控振荡器（</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">）产生本振信号，本振中心频率比</span></span><span lang="EN-US" style="color:#444444">FM</span><span style="font-family:宋体"><span style="color:#444444">信号标称值高一个中频频率，即</span></span><span lang="EN-US" style="color:#444444">48.5MHz+10.7MHz=59.2MHz</span><span style="font-family:宋体"><span style="color:#444444">。鉴频器输出信号中的直流成分用于控制</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">的振荡频率。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">当输入信号的载频高于标称值时，由于中频频率等于本振频率减去输入频率，故中频频率将随之下降。假设鉴相器的特性为前面图示的正向</span></span><span lang="EN-US" style="color:#444444">S</span><span style="font-family:宋体"><span style="color:#444444">曲线（注意鉴相器的</span></span><span lang="EN-US" style="color:#444444">S</span><span style="font-family:宋体"><span style="color:#444444">曲线可以是正向的也可以是反向的，取决于减法器的输入接法），鉴相器输出的平均电压将随之下降。此电压经过反相放大后加到</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">的控制端，使得</span></span><span lang="EN-US" style="color:#444444">VCO</span><span style="font-family:宋体"><span style="color:#444444">的振荡频率升高，从而维持中频频率基本不变。输入信号载频频率下降的情况可以得到同样结果。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">注意</span></span><span lang="EN-US" style="color:#444444">S</span><span style="font-family:宋体"><span style="color:#444444">曲线的正反向。如果采用的鉴频器是反向</span></span><span lang="EN-US" style="color:#444444">S</span><span style="font-family:宋体"><span style="color:#444444">曲线的，可以将放大器改为同相放大器。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span lang="EN-US" style="color:#444444">AFC</span><span style="font-family:宋体"><span style="color:#444444">电路的鉴频器输出中既包含了表示中频频率偏离的准直流电压，也包含了解调后的语音信号，反馈回路中的滤波</span></span><span lang="EN-US" style="color:#444444">-</span><span style="font-family:宋体"><span style="color:#444444">放大器的作用是取出其中的准直流信号，尽量衰减其中的语音信号（若语音信号反馈回去会降低其输出，即所谓的反调制现象）。所以此滤波电路的截止频率应该远低于音频信号的最低频率</span></span><span lang="EN-US" style="color:#444444">300Hz</span><span style="font-family:宋体"><span style="color:#444444">。考虑到题目要求漂移信号以</span></span><span lang="EN-US" style="color:#444444">2s</span><span style="font-family:宋体"><span style="color:#444444">为周期的三角波变化，这个滤波器的截止频率又要高于</span></span><span lang="EN-US" style="color:#444444">0.5Hz</span><span style="font-family:宋体"><span style="color:#444444">，综合考虑后可以在</span></span><span lang="EN-US" style="color:#444444">1~10Hz</span><span style="font-family:宋体"><span style="color:#444444">之间选取。例如选取</span></span><span lang="EN-US" style="color:#444444">3Hz</span><span style="font-family:宋体"><span style="color:#444444">，那么它对于</span></span><span lang="EN-US" style="color:#444444">300Hz</span><span style="font-family:宋体"><span style="color:#444444">的音频信号将有</span></span><span lang="EN-US" style="color:#444444">40dB</span><span style="font-family:宋体"><span style="color:#444444">的衰减量，可以认为已经足够了。</span></span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体"><span style="color:#444444">上述</span></span><span lang="EN-US" style="color:#444444">AFC</span><span style="font-family:宋体"><span style="color:#444444">电路在自动控制系统中称为</span></span><span lang="EN-US" style="color:#444444">0</span><span style="font-family:宋体"><span style="color:#444444">阶无差度控制系统，其特点是反馈控制信号依靠输出的误差信号维持，所以在输入信号频率漂移后，输出的中频频率还是有变化的。自动控制的目的是尽量减小这个输出频率的偏离。</span></span></span></span></span></span></p>
<p><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">设鉴频器的鉴频增益为</span></span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">K<sub>d</sub></span></span></span></i><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">（</span></span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">V/Hz</span></span></span><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">）、</span></span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">VCO</span></span></span><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">的压控增益为</span></span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">K<sub>o</sub></span></span></span></i><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">（</span></span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">Hz/V</span></span></span><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">）、反馈回路中的滤波</span></span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">-</span></span></span><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">放大器的直流增益为</span></span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">K<sub>a</sub></span></span></span></i><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">，根据负反馈理论可知，当输入信号的漂移频偏为</span></span></span><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">Δ</span></span></span><i><span lang="EN-US" style="font-size:10.5pt"><span style="font-family:"Times New Roman",serif"><span style="color:#444444">f<sub>S</sub></span></span></span></i><span style="font-size:10.5pt"><span style="font-family:宋体"><span style="color:#444444">时，中频变化量为</span></span></span></p>
<p> </p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">可见由于负反馈作用，输入信号的频率漂移被大幅度缩减。只要缩减后的载频漂移不影响中频放大器的放大、不影响鉴频器的鉴频，那么就可以认为这个接收机在载频漂移条件下能够正常工作。</span></span></span></span></span></p>
<p style="text-indent:21.0pt; text-align:justify"><span style="font-size:10.5pt"><span style="line-height:115%"><span style="layout-grid-mode:char"><span style="font-family:"Times New Roman",serif"><span style="font-family:宋体">本题目中输入载频漂移的最大值为</span>150kHz<span style="font-family:宋体">。假定</span>LC<span style="font-family:宋体">斜率鉴频器的有效鉴频范围为</span>±50kHz<span style="font-family:宋体">，在此范围内的输出为</span>±1.5V<span style="font-family:宋体">，则鉴频增益</span><i>K<sub>d</sub></i>=3<span style="font-family:宋体">×</span>10<sup>-5</sup><span style="font-family:宋体"><span style="color:#444444">（</span></span><span lang="EN-US" style="color:#444444">V/Hz</span><span style="font-family:宋体"><span style="color:#444444">）；假定</span></span>VCO<span style="font-family:宋体">在控制电压为</span>2.5V±1V<span style="font-family:宋体">时的频率变化为</span>±10MHz<span style="font-family:宋体">，则压控增益</span><i>K<sub>o</sub></i>=1<span style="font-family:宋体">×</span>10<sup>7</sup><span style="font-family:宋体"><span style="color:#444444">（</span></span><span lang="EN-US" style="color:#444444">Hz/V</span><span style="font-family:宋体"><span style="color:#444444">）</span></span><span style="font-family:宋体">；再假定滤波放大器的增益</span><i>K<sub>f</sub></i>=1<span style="font-family:宋体">，则</span><i>K<sub>d</sub>K<sub>f</sub>K<sub>o</sub></i>=300<span style="font-family:宋体">。已知输入信号的最大载频变化为</span>±150kHz<span style="font-family:宋体">，则在</span>AFC<span style="font-family:宋体">作用下的中频变化只有大约</span>±0.5kHz<span style="font-family:宋体">。只要中频放大器的通带宽度与鉴频器的有效鉴频范围均留有</span>±0.5kHz<span style="font-family:宋体">的裕量，就能保证在载频漂移的情况下正常接收。适当增加中频放大器的通带宽度与鉴频器的有效鉴频范围，就能满足题目中关于扩大输入载频漂移频率的提高要求。</span></span></span></span></span></p>
<p>不错</p>
页:
[1]