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外差混频法要求两束光信号振动方向相同,频率相差很小,幅度相等并且在同一方向传播,最后通过光电探测器拍频实现相移。两束光信号可分别表示为[18]:
$ \left\{\begin{array}{l}{E_{1}=A \cos \left(\omega_{1} t+\varphi_{1}\right)} \\ {E_{2}=A \cos \left(\omega_{2} t+\varphi_{2}\right)}\end{array}\right. $
(1) 式中,E是电场强度,A是光信号幅值,t是时间,ω是光信号角频率,φ是光信号相位。光信号在光电探测器上进行拍频可得:
$ \begin{array}{c}{E=E_{1}+E_{2}=A\left[\cos \left(\omega_{1} t+\varphi_{1}\right)+\right.} \\ {\cos \left(\omega_{2} t+\varphi_{2}\right) ]}\end{array} $
(2) 由和差化积公式,(2)式可以化简为:
$ \begin{array}{l} E = 2A\cos \left[ {\frac{1}{2}\left( {{\omega _1} + {\omega _2}} \right)t + \frac{1}{2}\left( {{\varphi _1} + {\varphi _2}} \right)} \right] \times \\ \cos \left[ {\frac{1}{2}\left( {{\omega _1} - {\omega _2}} \right)t + \frac{1}{2}\left( {{\varphi _1} - {\varphi _2}} \right)} \right] \end{array} $
(3) 令$\overline{\omega}=\frac{1}{2}\left(\omega_{1}+\omega_{2}\right), \omega_{\mathrm{m}}=\frac{1}{2}\left(\omega_{1}-\omega_{2}\right) $,则(3)式可以简化为:
$ \begin{aligned} E=& 2 A \cos \left[\overline{\omega} t+\frac{1}{2}\left(\varphi_{1}+\varphi_{2}\right)\right] \times \\ & \cos \left[\omega_{\mathrm{m}} t+\frac{1}{2}\left(\varphi_{1}-\varphi_{2}\right)\right] \end{aligned} $
(4) 令$ A_{\mathrm{m}}=2 A \cos \left[\omega_{\mathrm{m}} t+\frac{1}{2}\left(\varphi_{\mathrm{A}}-\varphi_{2}\right)\right]$,则(4)式可以简化为:
$ E=A_{\mathrm{m}} \cos \left[\overline{\omega} t+\frac{1}{2}\left(\varphi_{1}+\varphi_{2}\right)\right] $
(5) 因为两光信号频率相差很小,即${\omega _{\rm{m}}} \ll \bar \omega $,所以把叠加的信号视为载波频率为$ \bar \omega $的调幅波。
因为受到光电探测器的带宽限制,所以在光电探测器上的叠加混频信号只能显示出调制频率${\omega _{\rm{m}}} $,拍频后的光电流为:
$ I \propto A_{\mathrm{m}}^{2}=2 \alpha^{2}\left\{1+\cos \left[2 \omega_{\mathrm{m}} t+\left(\varphi_{1}-\varphi_{2}\right)\right]\right\} $
(6) 式中,α是延时线相位,为常数。把直流分量滤出,则(6)式可以简化为:
$ I_{\omega_{1}-\omega_{2}} \propto \cos \left[\left(\omega_{1}-\omega_{2}\right) t+\left(\varphi_{1}-\varphi_{2}\right)\right] $
(7) 从上述分析可得出,假设两束光信号中心频率满足条件:ω1-ω2=ωRF,光电探测器将两信号拍频后获得频率为ωRF的射频信号,并且通过调整φ1-φ2实现射频信号相移。所以通过调整两束光信号相位的φ1或者φ2,最终控制射频信号相位。
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相位调制的光信号的表达式可以化简为[19]:
$ \begin{array}{c}{E_{\mathrm{PM}}=E_{\mathrm{c}}\left\{\mathrm{J}_{0}\left(m_{\varphi}\right) \cos \left(\omega_{0} t\right)+\mathrm{J}_{1}\left(m_{\varphi}\right) \times\right.} \\ {\cos \left[\left(\omega_{0}+\omega^{\prime}\right) t+\frac{\pi}{2}\right]+} \\ {\mathrm{J}_{-1}\left(m_{\varphi}\right) \cos \left[\left(\omega_{0}-\omega^{\prime}\right) t-\frac{\pi}{2}\right] \}}\end{array} $
(8) 式中, 后两项分别对应+1阶边带和-1阶边带光场的表达式。Ec为载波信号幅值,t为时间,ω0为光载波信号的角频率,ω′为射频信号的角频率,mφ为调制系数,Jn(mφ)(n=-1,0,1)为贝塞尔函数。如果光电信号直接进入到光电探测器中,由于光电信号的1阶上边带和1阶下边带存在180°相位差,光电探测器无法检测到射频信号。图 3为相位调制后的载波和边带相位谱。如图 3a所示, 当调整相位调制器的相位为180°时,载波相位为90°,+1阶相位为90°,-1阶相位为-90°。如图 3b所示,当相位调制器相位为90°时,载波相位为45°,+1阶相位为45°,-1阶相位为-135°。即当相位调制器的相位θ°(0° < θ≤180°)时,载波相位为θ/2,+1阶相位为θ/2,由于(1阶边带相位差为180°,所以-1阶相位为-180°+θ/2。
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下式对应的是输入射频信号的电场表达式:
$ V_{\text { out }}=V_{\text { bias }}+V_{0} \sin (2 \pi f t+\mu) $
(9) 式中,Vout为输出电压值,Vbias为偏置电压值,E0为输入幅值,f为输入频率,μ为初始相位。仿真中设置V0=1V,初始相位μ=0°,偏置电压Vbias=0.5V,f=20GHz。图 4所示的是在输入射频信号为20GHz情况下输出的时域波形图。周期为0.05ns,当sin(2πft+μ)=0时,输出电压Vout=0.5V,当sin(2πft+μ)=1时,输出电压Vout=1.5V,当sin(2πft+μ)=-1时,输出电压Vout=-0.5V。
图 5所示的是在相位调制器角度为180°、延时线相位为90°的情况下,实现的带通滤波器的高斯1阶滤波器包络及带通滤波器前后的光谱图。图 5a所示的是带通滤波器的高斯1阶滤波器包络;图 5b所示的是滤波器前的光谱图,此时载波的功率为-3.6dBm,±1阶边带功率为-4.2dBm;图 5c所示的是滤波器后的光谱图,此时滤出的是+1阶边带信号,+1阶边带信号功率为-4.2dBm。
Figure 5. a—Gaussian first-order filter envelope of the implemented bandpass filter b—before filtering c—after filtering
图 6所示的是延时线分别为0°, 90°, 180°, 270°、相位调制器的相位为0°~180°时,输出射频信号的相位和功率谱图。射频信号相位范围分别为0°~90°(a曲线),-90°~0°(b曲线),-180°~-90°(c曲线),90°-180°(d曲线)。移相范围刚好满足0°~360°,功率变化范围均为-30dBm~-25dBm(f曲线)。
图 7所示的是输入射频信号为20GHz时的射频信号时域图。延时线分别为0°, 90°, 180°, 270°,相位调制器角度为180°时,功率值均为29.5dBm,功率基本保持不变。
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输入扫频信号为0GHz~40GHz,带通滤波器带宽仍为5GHz,滤波器的中心频率随扫频信号频率变化而变化,载波的中心频率fc加上扫频信号的频率fs等于滤波器的中心频率(fc+fs),其它条件保持不变的情况下,移相器相位谱图和功率谱图如图 8所示。图 8a所示的是移相器扫频相位谱图,通过改变光信号的载波和边带的相位,在保持射频信号功率值不变的情况下,实现射频信号的相位0°~360°可调。图 8b所示为移相器扫频功率谱图,延时线分别为0°, 90°, 180°, 270°、相位调制器角度为180°时,功率值均为29.5dBm,光电探测后射频信号功率保持不变。图 9所示的是激光器输入功率与输出射频信号功率关系。表明当激光器功率为0mW~100mW时,射频信号功率随激光器功率增加呈线性增长状态,射频信号功率范围为0mW~25mW。
基于载波和边带相位控制的微波光子移相器
Microwave photonic phase shifters based on phase control of optical carrier and sidebands
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摘要: 为了实现一种360°相移新型微波光子移相器,通过使用一个相位调制器、延迟线和光学滤波器来控制载波和边带的相位,最终控制射频信号的相位。相位调制器只需控制一个电压来调节移相角度,减少了使用复杂双平行马赫-曾德尔调制器所导致的漂移带来的影响,具有结构简单、成本较低等优点。结果表明,仿真验证的微波光子移相器可以在0GHz~40GHz频率范围内实现从0°~360°的全相移范围,并且在同一输出相位情况下,频率在0GHz~40GHz范围内,功率基本保持不变。此研究对微波光子移相器技术有一定参考意义。Abstract: In order to realize a novel microwave photon phase shifter with 360° phase shift, the phase of radio frequency signal was controlled by using a phase modulator, delay line and optical filter to control the phase of carrier and sideband. The phase modulator only needs to control a voltage to adjust the phase shift angle. The effect of drift caused by the use of complex dual-parallel Mach-Zehnder modulator (DPMZM) was reduced. The system had the advantages of simple structure and low cost. The results show that, the microwave photonic phase shifter can achieve full phase shifting from 0°~360° in the frequency range of 0GHz~40GHz. And at the same output phase and under the frequency ranges from 0GHz to 40GHz, the power is basically unchanged. This research has certain reference significance for microwave photonic phase shifter technology.
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Key words:
- optical communication /
- microwave photonic /
- phase shifter /
- phase modulator
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