频谱分析仪相位噪声测量原理ppt课件

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频谱分析仪的工作原理和使用方法ppt课件

频谱分析仪的工作原理和使用方法ppt课件

3.2 选择性
3 dB
3 dB BW
60 dB 60 dB BW 60 dB BW 3 dB BW


节到混频器的最佳信号电平,已防止发生混频压缩和失真。 信号经过预选器和低通滤波器进入混频器。 信号经过混频后,在其输出端有原来的信号、本振信号,两个输入信号 的和频信号/差频信号,以及其他高次谐波信号。通常我们取其差频信号, 称之为中频信号。 中频滤波器滤出中频信号并进行放大。 中频信号经检波和视频滤波后加到显示器上进行显示,视频滤波器的作 用是对显示屏上所显示的扫迹进行平均或平滑。 频谱仪所显示的谱线是被测信号叠加上频谱仪内部的噪声的总效应。为 了减小噪声对信号幅度的影响,要对经检波后的信号进行视频滤波或视 频平均。 当所选择的视频带宽等于或小于所选择的分辨力带宽(RBW)时,视频电 路的响应已经跟不上中频电路信号的变化,因此对所显示的信号就进行 了平均和平滑,两者之间的比值越小,平滑的效果越好。 视频平均是智能频谱仪为平滑提供的另一种选择。它对多次扫描的数据 逐点进行平均,因此显示的谱线更加平滑。
镜像频率干扰
频谱仪是一台超外差式接收机,它
的混频器是宽带的,因此在用频谱 仪测量信号时除了出现所需的信号 频率谱线外,还会显示出不需要的 镜像频谱。如图所示只要满足;,条 件时,和都会出现在频谱仪的显示 屏幕上,这就是镜像频率干扰。 有两种方案可以抑制镜像频率响应 的干扰:采用预选器和上变频的高 中频。
3.1 分辨力带宽 (RBW)
混频器 3 dB BW
输入频谱
3 dB
检波器
LO
本振
中频滤波器/分辨率带宽滤波器 扫频
分辨率 带宽 显示
3.1 分辨力带宽 (RBW)
10 kHz RBW 3 dB

第三章 噪声测量方法 ppt课件

第三章 噪声测量方法 ppt课件

第三章 噪声测量方法
城市环境噪声的特点:随时间起伏较大、无规律、具有 较大的随机性。
噪 声 测 量 方 法:等时抽样技术

类: 城市区域环境噪声普查方法 交通噪声测量 城市噪声长期监测
第三章 噪声测量方法
测点确定: 将市区划分为等距离的网格(500×500米,250 × 250米), 数目多于100个,测点选在网格中心
修正值(分贝)
第三章 噪声测量方法
8 7 6 5 4 3 2 1 0
1 2 3 4 5 6 7 8 9 10 总的噪声与背景噪声之差(分贝)
由图中可以看出, 总噪声与背景噪声 相差越小,修正值 越大,说明背景噪 声对其影响越大。
例如:测量某发动机噪声,当发动机未开时,测得背景噪 声为76分贝,开动发动机测得总声级为80分贝,两者之差 为4分贝,修正值为2分贝,则发动机的噪声值为78分贝。
第三章 噪声测量方法
生产环境(车间)噪声测量 工业企业现场机器噪声的测量
第三章 噪声测量方法
测点:
在操作人员经常所在的位置或观察生产过程而经常工 作、活动的范围内,以人耳高度为准,使用“慢”特 性 车间内声级分布差异小于3分贝,选择1~3个测点 声级分布差异大于3分贝,按声级大小将车间分成若干 区域,区域内声级差异小于3分贝,相邻区域声级差异 大于或等于3分贝,在每个区域取1~3个测点测量

抚顺路
>50m
抚顺路


20cm
声级计用法:
传声器距离地面高1.2米,垂直指向公路。 使用“慢”特 性,每5秒钟读一个数,连续读200个数。 记录车流量。
计算:等效连续A声级Leq
LeqL50
(L10
L90)2 60

现代电子测量频谱分析仪PPT课件

现代电子测量频谱分析仪PPT课件
5
频谱分析仪
频谱分析仪的用途
信号的频谱分析; 信号的基本参数测量; 频率稳定度的测试; 配接天线后用作场强仪,用于EMC测量; 网络测量;
6
频谱分析仪
频谱分析仪的用途
低频频谱分析仪广泛应用于声频、振动与冲击、 机械工程、建筑、医学等领域;
以FFT为核心的频谱仪能提供包括相位谱在内 的各种频谱,可用于信号的时域、领域、幅值 域的各种分析;
22
频谱分析仪
频谱分析仪的频率分辨率
滤波器的半功率带宽及有效噪声带宽
半功率带宽即为3dB带宽; 当理想的矩形滤波器在矩 形曲线下的面积与实际滤波 器特性曲线下的面积相等时, 矩形的宽度即为实际滤波器 有效噪声带宽; 常用3dB带宽来代替有效 噪声带宽。
23
频谱分析仪
频谱分析仪的频率分辨率
滤波器的半功率带宽及有效噪声带宽
12
频谱分析仪
频谱分析仪的工作原理
目前微波或 高频频谱分析仪 普遍采用的是扫 频超外差的测试 原理, 简化原理 框图如右图所示
13
频谱分析仪
频谱分析仪的工作原理
频谱分析的 过程如右图所示
14
频谱分析仪
频谱分析仪的工作原理
包络检波器:频谱仪显示的是经包络检波器后的视频信号,检 波器应跟随 IF信号的包络而变化,而不是随 IF正弦波本身的 瞬时值而变。
54
频谱分析仪
频谱仪使用中的问题
第一级混频器过载造成的失真 当输入信号的幅度超过了混频电路的最大线性范围时, 其输出的幅度就会比正常值低,并且由于交调或谐波失真 而产生出许多不需要的信号; 对于一般的频谱分析仪,加到第一级混频器上的最佳信 号幅度约为+17dBmV;
55
频谱分析仪

声学噪音频谱分析PPT课件

声学噪音频谱分析PPT课件

SpectraLAB可以运行多个实例 因此我们再开启一个 并在打开一个wav文件 流程同上
金在升440电机,103VS131
这里,你能看到哪些差别
哦,时间域的幅值
频谱分析
在频谱图上右键,copy as text 将数据拷贝到excel处理,数据量为2027行 将另一个声音文件测频谱数据做同样处理 因为频率一列总是相同的 一般的,左声道和右声道数据也相同 多个语音文件汇总,我们能得到不同语音
block1stbuildingbaiwangrdbuilding5158thshahewestroadnanshandistrictshenzhenprchina声级计为了用仪器直接测出反映人对噪声的响度感觉便从等响曲线中选取了40方70方100条曲线按这三条曲线的反曲线设计了由电阻电容等电子器件组成的计权网络设置在声级计上使声级计分别具有a主流的为a计权声级计一些声级计也有频谱分析功能因资源有限只能选取10个左右的频率szfrge005a04cn2017foreach深圳市恒永达科技有限公司深圳市南山区沙河西路5158号百旺研发大厦114thfl
的频谱对比
泵噪音测试
典型的,可以给分贝数dBA,感觉就是有 异常,但不会评价,怎么办?
录音——频谱分析
录音的要求
要一致要公正,要有夹具,录音的位置、距离、 方向要一致
异音的原因是什么?
估计是轴承
金在升440电机,103VS131
这里,你能看到哪些差别 哦,红色的总是高
音频频谱
提示,电机最高速度为1500PPS
主流的为A计权声级计 dBA
给了一个加权后的结果,对声音的品质无从评 价
一些声级计也有频谱分析功能,因资源有限, 只能选取10个左右的频率

[课件]频谱分析仪基础PPT

[课件]频谱分析仪基础PPT

影响频谱仪灵敏度的主要因素
VBW影响显示
VBW影响显示 噪声电平的方差, 减小VBW得到其 平均值, 减小VBW有利于 在噪声背景下检 测CW信号。
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频谱分析仪的性能指标
内部失真
2018/12/4
频谱分析仪产生内部失真的原因
混频器以及内部其它电路产生的非线性失真
2018/12/4
3. VBW设置为最小。
4.前置放大器的噪声系数最小。(增益大 于噪声系数)
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改变衰减器
来判断频谱仪测试结果的真实性。
2018/12/4
提高频谱仪幅度测量精度的方法
内部自校 设置参考电平,使被测信号电平尽可能接近参考电平 频响误差修正
2018/12/4
提高频谱仪频率测量精度的方法
本振相位噪声在频域上表现为信号频谱的噪声边带
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频谱仪测试的灵敏度
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影响频谱仪灵敏度的主要因素
衰减器设置
衰减器设置值 越大,噪声电 平越高。
2018/12/4
影响频谱仪灵敏度的主要因素
RBW
噪声电平随RBW按照
10logRBW1/RBW2
规律变化
2018/12/4
计数器功能
计数器方式下,频谱仪频率测量精度和扫频宽度无关。
2018/12/4
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附录
采样频率决定了测量信号的最大带宽。
频谱分析仪测量信号的频率信息,包括频率,功
率,谐波失真,杂波干扰,信号的相位噪声谱,
器件的噪声系数高级的频谱分析仪还可以实现对

频谱分析仪测量和噪声(AN 1303)

频谱分析仪测量和噪声(AN 1303)

AgilentSpectrum and Signal Analyzer Measurements and NoiseApplication Note 1303Measuring Noise and Noise-like DigitalCommunications Signals with Spectrum and Signal Analyzers3 3 3 3 6 7 8 8 9 101214 14 14 16 16 17 18 18 19 19 19 19 19 20 21 2223 23 24 25 27 28Table of ContentsPart I: Noise Measurements IntroductionSimple noise—Baseband, Real, Gaussian Bandpassed noise—I and QMeasuring the power of noise with an envelope detector Logarithmic processingMeasuring the power of noise with a log-envelope scale Equivalent noise bandwidth The noise markerSpectrum analyzers and envelope detectorsCautions when measuring noise with spectrum and Signal analyzersPart II: Measurements of Noise-like Signals The noise-like nature of digital signalsChannel-power measurements Adjacent-Channel Power (ACP)Carrier power Peak-detected noise and TDMA ACP measurements Part III: Averaging and the Noisiness of Noise MeasurementsVariance and averagingAveraging a number of computed resultsSwept versus FFT analysis Zero spanAveraging with an average detectorMeasuring the power of noise with a power envelope scale The standard deviation of measurement noise ExamplesThe standard deviation of CW measurements Part IV: Compensation for Instrumentation Noise CW signals and log versus power detectionPower-detection measurements and noise subtraction Log scale ideal for CW measurements Bibliography Glossary of Terms2IntroductionNoise. It is the classical limitation of electronics.In measurements, noise and distortion limit the dynamic range of test results.In this four-part paper, the characteristics of noise and its direct measurement are discussed in Part I. Part II contains a discussion of the measurement of noise-like signals exemplified by digital CDMA and TDMA signals. Part III discusses using averaging techniques to reduce noise. Part IV is about compensating for the noise in instrumentation while measuring CW (sinusoidal) and noise-like signals.Simple noise—Baseband, Real, GaussianNoise occurs due to the random motion of electrons. The number of electrons involved is large, and their motions are independent. Therefore, the variation in the rate of current flow takes on a bell-shaped curve known as the Gaussian Probability Density Function (PDF) in accordance with the central limit theorem from statistics. The Gaussian PDF is shown in Figure 1.The Gaussian PDF explains some of the characteristics of a noise signal seen on a baseband instrument such as an oscilloscope. The baseband signal is a real signal; it has no imaginary components.Bandpassed noise—I and QIn RF design work and when using spectrum analyzers, we usually deal with signals within a passband, such as a com-munications channel or the resolution bandwidth (RBW, the bandwidth of the final IF) of a spectrum analyzer. Noise in this bandwidth still has a Gaussian PDF, but few RF instruments display PDF-related metrics.Instead, we deal with a signal’s magnitude and phase (polar coordinates) or I/Q components. The latter are the in-phase (I) and quadrature (Q) parts of a signal, or the real and imaginary components of a rectangular-coordinate representation of a signal. Basic (scalar) spectrum analyzers measure only the magnitude of a signal. We are interested in the characteristics of the magnitude of a noise signal.Part I: Noise Measurements3Figure 1. The Gaussian PDF is maximum at zero current and falls off away from zero,as shown (rotated 90 degrees) on the left. A typical noise waveform is shown on the right.We can consider the noise within a passband as being made of independent I and Q components, each with Gaussian PDFs. Figure 2 shows samples of I and Q com-ponents of noise represented in the I/Q plane. The sig-nal in the passband is actually given by the sum of the I magnitude, v I , multiplied by a cosine wave (at the center frequency of the passband) and the Q magnitude, v Q , mul-tiplied by a sine wave. But we can discuss just the I and Q components without the complications of the sine/cosine waves.Spectrum analyzers respond to the magnitude of the signal within their RBW passband. The magnitude, or envelope, of a signal represented by an I/Q pair is given by:v env =√(v I 2+v Q 2)Graphically, the envelope is the length of the vector from the origin to the I/Q pair. It is instructive to draw circles of evenly spaced constant-amplitude envelopes on the samples of I/Q pairs as shown in Figure 3.Figure 2. Bandpassed noise has a Gaussian PDF independently in both its I and Q components.–3–2–10123–3–2–1123–3–2–10123–3–2–101234If one were to count the number of samples within each annular ring in Figure 3, we would see that the area near zero volts does not have the highest count of samples. Even though the density of samples is highest there, this area is smaller than any of the other rings.The count within each ring constitutes a histogram of the distribution of the envelope. If the width of the rings were reduced and expressed as the count per unit of ring width, the limit becomes a continuous function instead of a histo-gram. This continuous function is the PDF of the envelope of bandpassed noise. It is a Rayleigh distribution in the envelope voltage, v, that depends on the sigma of the sig-nal; for v greater than or equal to 0PDF (v)= (v–σ2)exp (–1—2 (v–σ)2)The Rayleigh distribution is shown in Figure 4.Figure 3. Samples of I/Q pairs shown with evenly spaced constant-amplitude envelope circlesFigure 4. The PDF of the voltage of the envelope of a noise signal is a Rayleigh distribution.The PDF is zero at zero volts, even though the PDFs of the individual I and Q components aremaximum at zero volts. It is maximum for v=sigma.5Measuring the power of noise with an envelope detectorThe power of the noise is the parameter we usually want to measure with a spectrum analyzer. The power is the heating value of the signal. Mathematically, it is the time-average of v2(t)/R, where R is the impedance and v(t) is the voltage at time t.At first glance, we might like to find the average enve-lope voltage and square it, then divide by R. But finding the square of the average is not the same as finding the average of the square. In fact, there is a consistent under-measurement of noise from squaring the average instead of averaging the square; this under-measurement is 1.05 dB The average envelope voltage is given by integrating the product of the envelope voltage and the probability that the envelope takes on that voltage. This probability is theThe average power of the signal is given by an analogous expression with v2/R in place of the "v" part:p–= ∫∞(v–R2)PDF(v)dv =2σ–R2We can compare the true power, from the average power integral, with the voltage-envelope-detected estimate ofv2/R and find the ratio to be 1.05 dB, independent of s andThus, if we were to measure noise with a spectrum analyzer using voltage-envelope detection (the linear scale) and averaging, an additional 1.05 dB would need to be added to the result to compensate for averaging voltage instead of voltage-squared.6Logarithmic processingSpectrum Analyzers are most commonly used in their logarithmic (log) display mode, in which the vertical axis is calibrated in decibels. Let us look again at our PDF for the voltage envelope of a noise signal, but let’s mark the x-axis with points equally spaced on a decibel scale, in this case with 1 dB spacing. See Figure 5. The area under the curve between markings is the probability that the logof the envelope voltage will be within that 1 dB interval. Figure 6 represents the continuous PDF of a logged signal which we predict from the areas in Figure 5.Figure 6. The PDF of logged noise is about 30 dB wide and tilted toward the high end.7Measuring the power of noise with alog-envelope scaleWhen a spectrum analyzer is in a log (dB) displaymode, averaging of the results can occur in numerous ways. Multiple traces can be averaged, the envelope can be aver-aged by the action of the video filter, or the noise marker (more on this below) averages results across the x-axis. Some recently introduced analyzers also have a detector that averages the signal amplitude for the duration of a measurement cell.When we express the average power of the noise in deci-bels, we compute a logarithm of that average power. When we average the output of the log scale of a spectrum analyzer, we compute the average of the log. The log of the average is not equal to the average of the log. If we go through the same kinds of computations that we did com-paring average voltage envelopes with average power envelopes, we find that log processing causes an under-response to noise of 2.51 dB, rather than 1.05 dB.1The log amplification acts as a compressor for large noise peaks; a peak of ten times the average level is only 10 dB higher. Instantaneous near-zero envelopes, on the other hand, contain no power but are expanded toward negative infinity decibels. The combination of these two aspects of the logarithmic curve causes noise power to measure lower than the true noise power.Equivalent noise bandwidthBefore discussing the measurement of noise with a spec-trum analyzer noise marker, it is necessary to understand the RBW filter of a spectrum analyzer.The ideal RBW has a flat passband and infinite attenuation outside that passband. But it must also have good time domain performance so that it behaves well when signals sweep through the passband. Most spectrum analyzers use four-pole synchronously tuned filters for their RBW filters. We can plot the power gain (the square of the voltage gain) of the RBW filter versus frequency as shown in Figure 7. The response of the filter to noise of flat power spectral density will be the same as the response of a rectangular filter with the same maximum gain and the same areaunder their curves. The width of such a rectangular filter is the equivalent noise bandwidth of the RBW filter. The noise density at the input to the RBW filter is given by the output power divided by the equivalent noise bandwidth.1. Most authors on this subject artifi cially state that this factor is due to1.05 dB from envelope detection and another 1.45 dB from logarithmicamplifi cation, reasoning that the signal is fi rst voltage-envelopedetected, then logarithmically amplifi ed. But if we were to measure the voltage-squared envelope (in other words, the power envelope, which would cause zero error instead of 1.05 dB) and then log it, we wouldstill fi nd a 2.51 dB under-response. Therefore, there is no real point in separating the 2.51 dB into two pieces.8The ratio of the equivalent noise bandwidth to the –3 dB bandwidth (An RBW is usually identified by its –3 dB BW) is given by the following table:Filter type Application NBW/–3 dB BW4-pole sync Most SAs analog 1.128 (0.52 dB)5-pole sync Some SAs analog 1.111 (0.46 dB)Typical FFT FFT-based SAs 1.056 (0.24 dB)The noise markerAs discussed above, the measured level at the out put of a spectrum analyzer must be manipulated in order to repre-sent the input spectral noise density we wish to measure. This manipulation involves three factors, which may be added in decibel units:1. Under-response due to voltage envelope detection (add1.05 dB) or log-scale response (add2.51 dB).2. Over-response due to the ratio of the equivalent noisebandwidth to the –3 dB bandwidth (subtract 0.52 dB). 3. Normalization to a 1 Hz bandwidth (subtract 10 timesthe log of the RBW, where the RBW is given in unitsof Hz).Most spectrum analyzers include a noise marker that accounts for the above factors. To reduce the variance of the result, the Agilent 8590 and 8560 families of spectrum analyzers compute the average of 32 trace points cen-tered around the marker location. The Agilent ESA family, which allows you to select the number of points in a trace, compute the average over one half of a division centeredat the marker location. For an accurate measurement, you must be sure not to place the marker too close to a discrete spectral component.The final result of these computations is a measure of the noise density, the noise in a theoretical ideal 1 Hz band-width. The units are typically dBm/Hz.Figure 7. The power gain versus frequency of an RBW filter can be modeled by a rectangular filterwith the same area and peak level, and a width of the “equivalent noise bandwidth.”9Spectrum analyzers and envelope detectorsA simplified block diagram of a spectrum analyzer is shown in Figure A.The envelope detector/logarithmic amplifier block is shown configured as they are used in the Agilent 8560 E-Series spectrum analyzers. Although the order of these two cir-cuits can be reversed, the important concept to recognize is that an IF signal goes into this block and a baseband signal (referred to as the “video” signal because it was used to deflect the electron beam in the original analog spectrum analyzers) comes out.Notice that there is a second set of detectors in the block diagram: the peak/pit/sample hardware of what is normally called the detector mode of a spectrum analyzer. These display detectors are not relevant to this discussion, and should not be confused with the envelope detector.The salient features of the envelope detector are two:1. The output voltage is proportional to the input voltage envelope.2. The bandwidth for following envelope variationsis large compared to the widest RBW.Figure A. Simplified spectrum analyzer block diagramFigure B. Detectors: a) half-wave, b) full-wave implemented as a “product detector,” c) peak. Practical implementations usually have their gain terms implemented elsewhere, and implement buffering after the filters that remove the residual IF carrier and harmonics. The peak detector must be cleared; leakage through a resistor or a switch with appropriate timing are possible clearing mechanisms.10Figure B shows envelope detectors and their associated waveforms in (a) and (b). Notice that the gain required to make the average output voltage equal to the r.m.s. voltage of a sinusoidal input is different for the different topologies. Some authors on this topic have stated that “an envelope detector is a peak detector.” After all, an idealized detector that responds to the peak of each cycle of IF energy inde-pendently makes an easy conceptual model of ideal behav-ior. But real peak detectors do not reset on each IF cycle. Figure B, part c, shows a typical peak detector with its gain calibration factor. It is called a peak detector because its response is proportional to the peak voltage of the signal. If the signal is CW, a peak detector and an envelope detec-tor act identically. But if the signal has variations in its envelope, the envelope detector with the shown LPF (low pass filter) will follow those variations with the linear, time-domain characteristics of the filter; the peak detector will follow nonlinearly, subject to its maximum negative-going limit, as demonstrated in Figure C. The nonlinearity will make for unpredictable behavior for signals with noise-like statistical variations. A peak detector may act like an envelope detector in the limit as its resistive load dominates and the capacitive load is minimized. But practically, the nonideal voltage drop across the diodes and the heavy required resistive load make this topology unsuitable for envelope detection. All spectrum analyzers use envelope detectors, some are just misnamed.Figure C. An envelope detector will follow the envelope of the shown signal, albeit with the delay and filtering action of the LPF used to remove the carrier harmonics. A peak detector is subject to negative slew limits, as demonstrated by the dashed line it will follow across a response pit. This drawing is done for the case in which the logarithmic amplification precedes the envelope detection, oppositeto Figure A; in this case, the pits of the envelope are especially sharp.Cautions when measuring noise with spectrum and signal analyzersThere are three ways in which noise measurements can look perfectly reasonable on the screen of a spectrum ana-lyzer, yet be significantly in error.Caution 1, input mixer level. A noise-like signal of very high amplitude can overdrive the front end of a spectrum ana-lyzer while the displayed signal is within the normal display range. This problem is possible whenever the bandwidth of the noise-like signal is much wider than the RBW. The power within the RBW will be lower than the total power by about ten times the log of the ratio of the signal band-width to the RBW. For example, an IS-95 CDMA signal with a 1.23 MHz bandwidth is 31 dB larger than the power in a 1 kHz RBW. If the indicated power with the 1 kHz RBW is –20 dBm at the input mixer (i.e., after the input attenuator), then the mixer is seeing about +11 dBm. Most spectrum analyzers are specified for –10 dBm CW signals at their input mixer; the level below which mixer compression is specified to be under 1 dB for CW signals is usually 5 dB or more above this –10 dBm. The mixer behavior with Gaussian noise is not guaranteed, especially because its peak-to-average ratio is much higher than that of CW signals.Keeping the mixer power below –10 dBm is a good practice that is unlikely to allow significant mixer nonlinearity. Thus, caution #1 is: Keep the total power at the input mixer at or below –10 dBm.Figure D. In its center, this graph shows three curves: the ideal log amp behavior, that of a log amp that clips at its maximum and minimum extremes, and the average response to noise subject to that clipping. The lower right plot shows, on expanded scales, the error in average noise response due to clipping at the positive extreme. The average level should be kept 7 dB below the clipping level for an error below 0.1 dB. The upper left plot shows, with an expanded vertical scale, the corresponding error for clipping against the bottom of the scale. The average level must be kept 14 dB above the clipping level for an error below 0.1 dB.Caution 2, overdriving the log amp. Often, the level dis-played has been heavily averaged using trace averaging or a video bandwidth (VBW) much smaller than the RBW. In such a case, instantaneous noise peaks are well above the displayed average level. If the level is high enough that the log amp has significant errors for these peak levels, the average result will be in error. Figure D shows the error due to overdriving the log amp in the lower right corner, based on a model that has the log amp clipping at the topof its range. Typically, log amps are still close to ideal for a few dB above their specified top, making the error model conservative. But it is possible for a log amp to switch from log mode to linear (voltage) behavior at high levels,in which case larger (and of opposite sign) errors to those computed by the model are possible. Therefore, caution #2 is: Keep the displayed average log level at least 7 dB below the maximum calibrated level of the log amp.Caution 3, underdriving the log amp. The opposite of the overdriven log amp problem is the underdriven log amp problem. With a clipping model for the log amp, the results in the upper left corner of Figure D were obtained. Caution #3 is: Keep the displayed average log level atleast 14 dB above the minimum calibrated levelof the log amp.In Part I, we discussed the characteristics of noise and its measurement. In this part, we will discuss three different measurements of digitally modulated signals, after showing why they are very much like noise.The noise-like nature of digital signalsDigitally modulated signals can be created by clocking a Digital-to-Analog Converter (DAC) with the symbols (a group of bits simultaneously transmitted), passing the DAC output through apre-modulation filter (to reduce the trans-mitted bandwidth), and then modulating the carrier with the filtered signal. See Figure 8. The resulting signal is obvi-ously not noise-like if the digital signal is a simple pattern. It also does not have a noise-like distribution if the band-width of observation is wide enough for the discrete nature of the DAC outputs to significantly affect the distribution of amplitudes.But, under many circumstances, especially test conditions, the digital signal bits are random. And, as exemplified by the channel power measurements discussed below, the observation bandwidth is narrow. If the digital update period (the reciprocal of the symbol rate) is less than one-fifth the duration of the majority of the impulse response of the resolution bandwidth filter, the signal within the RBW is approximately Gaussian according to the central limit theorem.A typical example is IS-95 CDMA. Performing spectrum analysis, such as the adjacent-channel power ratio (ACPR) test, is usually done using the 30 kHz RBW to observe the signal. This bandwidth is only one-fortieth of the symbol clock rate (1.23 Msymbols/s), so the signal in the RBW is the sum of the impulse responses to about forty pseudo-random digital bits. A Gaussian PDF is an excellent approxi-mation to the PDF of this signal.Channel-power measurementsMost modern spectrum analyzers allow the measurement of the power within a frequency range, called the channel bandwidth. The displayed result comes from the computa-tion:P ch =(B s–B n)(1–N) n2i=n1∑10(p i/10)Pch is the power in the channel, Bs is the specified bandwidth (also known as the channel bandwidth), Bnis the equivalent noise bandwidth of the RBW used, Nis the number of data points in the summation, pi is the sample of the power in measurement cell i in dB units (if pi is in dBm, Pch is in milliwatts). n1 and n2 are the end-points for the index i within the channel bandwidth, thus N=(n2 – n1) + 1.Part II: Measurements of Noise-like Signals Figure 8. A simplified model for the generation of digital communications signals.The computation works well for CW signals, such as from sinusoidal modulation. The computation is a power-sum-ming computation. Because the computation changes the input data points to a power scale before summing, there is no need to compensate for the difference between the log of the average and the average of the log as explained in Part I, even if the signal has a noise-like PDF (probability density function). But, if the signal starts with noise-like statistics and is averaged in decibel form (typically with a VBW filter on the log scale) before the power summation, some 2.51 dB under-response, as explained in Part I,will be incurred. If we are certain that the signal is of noise-like statistics, and we fully average the signal before per-forming the summation, we can add 2.51 dB to the result and have an accurate measurement. Furthermore, the aver-aging reduces the variance of the result.But if we don’t know the statistics of the signal, the best measurement technique is to do no averaging before power summation. Using a VBW ≥ 3RBW is required for insignifi-cant averaging, and is thus recommended. But the band-width of the video signal is not as obvious as it appears.In order to not peak-bias the measurement, the detector must be used. Spectrum analyzers have lower effective video bandwidths in sample detection than they do in peak detection mode, because of the limitations of the sample-and-hold circuit that precedes the A/D converter. Examples include the Agilent 8560E-Series spectrum analyzer family with 450 kHz effective sample-mode video bandwidth, and a substantially wider bandwidth (over 2 MHz) in the Agilent ESA-E Series spectrum analyzer family.Figure 9 shows the experimentally determined relationship between the VBW:RBW ratio and the under-response of the partially averaged logarithmically processed noise sig-nal.However, the Agilent PSA is an exception to the relation-ship illustrated by Figure 9. The Agilent PSA allows us to directly average the signal on a power scale. Therefore, if we are not certain that our signal is of noise-like statistics, we are no longer prohibited from averaging before power summation. The measurement may be taken by either using VBW filtering on a power scale, or using the average detec-tor on a power scale.Figure 9. For VBW ≥ 3 RBW, the averaging effect of the VBW filter does not significantly affect power-detection accuracy.Adjacent-Channel Power (ACP)There are many standards for the measurement of ACP with a spectrum analyzer. The issues involved in most ACP measurements are covered in detail in an article in Microwaves & RF, May, 1992, "Make Adjacent-Channel Power Measurements." A survey of other standards is available in "Adjacent Channel Power Measurements in the Digital Wireless Era" in Microwave Journal, July, 1994.For digitally modulated signals, ACP and channel-power measurements are similar, except ACP is easier. ACP is usually the ratio of the power in the main channel to the power in an adjacent channel. If the modulation is digital, the main channel will have noise-like statistics. Whether the signals in the adjacent channel are due to broadband noise, phase noise, or intermodulation of noise-like signals in the main channel, the adjacent channel will have noise-like statistics. A spurious signal in the adjacent channelis most likely modulated to appear noise-like, too, but a CW-like tone is a possibility.If the main and adjacent channels are both noise-like, then their ratio will be accurately measured regardless of whether their true power or log-averaged power (or any partially averaged result between these extremes) is mea-sured. Thus, unless discrete CW tones are found in the signals, ACP is not subject to the cautions regarding VBW and other averaging noted in the section on channel power above.But some ACP standards call for the measurement of abso-lute power, rather than a power ratio. In such cases, the cautions about VBW and other averaging do apply.Carrier powerBurst carriers, such as those used in TDMA mobile sta-tions, are measured differently than continuous carriers. The power of the transmitter during the time it is on is called the "carrier power."Carrier power is measured with the spectrum analyzerin zero span. In this mode, the LO of the analyzer doesnot sweep, thus the span swept is zero. The display then shows amplitude normally on the y axis, and time on the x axis. If we set the RBW large compared to the bandwidth of the burst signal, then all of the display points include all of the power in the channel. The carrier power is computed simply by averaging the power of all the display points that represent the times when the burst is on. Depending on the modulation type, this is often considered to be any point within 20 dB of the highest registered amplitude. (A trig-ger and gated spectrum analysis may be used if the carrier power is to be measured over a specified portion of a burst-RF signal.)Using a wide RBW for the carrier-power measurement means that the signal will not have noise-like statistics. It will not have CW-like statistics, either, so it is still wise to set the VBW as wide as possible. But let’s consider some examples to see if the sample-mode bandwidthsof spectrum analyzers are a problem.For PDC, NADC and TETRA, the symbol rates are under25 kb/s, so a VBW set to maximum will work well. It will also work well for PHS and GSM, with symbol rates of 380 and 270 kb/s. For IS-95 CDMA, with a modulation rate of 1.23 MHz, we could anticipate a problem with the 450 kHz effective video bandwidth discussed in the section on chan-nel power above. Experimentally, an instrument with 450 kHz BW experienced a 0.6 dB error with an OQPSK (mobile) burst signal.。

频谱分析仪相位噪声测量原理(图文)

频谱分析仪相位噪声测量原理(图文)

频谱分析仪相位噪声测量原理(图文)论文导读:相位噪声是衡量信号源频稳质量的主要技术指标,专用的相位噪声测试系统设备量庞大,价格昂贵,用频谱分析仪测量相位噪声是一种简单直接的测量方法,而频谱分析仪作为通用的测量仪器,广泛应用于普通实验室和雷达、通信、电子设备的生产使用中。

针对某频谱仪开发的相位噪声测试选件不仅能为用户自动完成相位噪声测量功能,并提供多样化的测试报表,使相位噪声的测量变得简单、快捷。

关键词:频谱分析仪,相位噪声1引言相位噪声是衡量信号源频稳质量的主要技术指标,专用的相位噪声测试系统设备量庞大,价格昂贵,用频谱分析仪测量相位噪声是一种简单直接的测量方法,而频谱分析仪作为通用的测量仪器,广泛应用于普通实验室和雷达、通信、电子设备的生产使用中。

随着现代频谱分析仪性能(动态范围、分辨率、内部噪声)的不断提高,给直接频谱分析法创造了有利条件。

针对某频谱仪开发的相位噪声测试选件不仅能为用户自动完成相位噪声测量功能,并提供多样化的测试报表,使相位噪声的测量变得简单、快捷。

本文重点介绍了用频谱分析仪测量相位噪声的原理与相噪选件的实现。

2相位噪声的基本概念频率稳定度是信号源的重要指标,指在一定的时间间隔内,信号源输出频率的变化。

根据时间间隔的长短可分为长期稳定度和短期稳定度。

短期稳定度在时域表现为在波形零点处的抖动,可以用相对频率起伏(阿伦方差)来描述,在频域则用相位噪声来表征。

一个有幅度和频率起伏的正弦波可表示为:υ(t)= [V0 +a(t)]sin[2πf0t+φ(t)] (1)式中a(t)= 幅度噪声,φ(t)= 相位噪声通常信号源输出的信号都会有调幅噪声a(t) <<V0,它不直接造成频率起伏或相位起伏,不影响频率稳定度,在这里可以忽略不计。

信号的噪声边带主要由调相噪声引起,实际测量中常用单边带相位噪声(SSB)来表示短期频率稳定度,美国国家标准局把SSB相位噪声(L(ƒm))定义为:偏离载波频率ƒm Hz,在1Hz带宽内一个相位调制边带的功率PSSB与总的信号功率Ps之比,即L(ƒm)= = (2)L(ƒm)是相位噪声最常用的表示形式,通常用相对于载波波段1Hz带宽的对数表示(dBc/Hz)。

《频谱分析仪讲》课件

《频谱分析仪讲》课件

航空航天
在航空航天领域, 频谱分析仪被广泛 应用于飞行器通信 和雷达系统的频谱 分析和故障诊断。
电磁兼容性 测试
频谱分析仪可以用 于评估电磁兼容性, 检测和分析电子设 备之间的干扰情况。
音频分析
音频分析包括音频 信号的频谱分布、 谐波失真、杂散和 噪声等特性的分析。
五、频谱分析仪的市场现状与趋势
1 全球频谱分析仪市
分析范围不足
分析范围可以通过选用具有更大频率范围的 频谱分析仪来解决。
信号干扰
信号干扰可能会影响频谱分析结果,可以通 过优化测量环境、屏蔽干扰源等方式来解决。
校准问题
频谱分析仪的校准非常重要,可以定期进行 校准或选择具备自动校准功能的仪器。
七、总结与展望
频谱分析仪的发展 历程
频谱分析仪经过多年的发展, 已经成为电子测量领域中不 可或缺的重要工具。
未来发展方向
未来频谱分析仪将继续向更 高频率、更高精度、更智能 化的方向发展。
重点关注领域
未来频谱分析仪在5G通信、 物联网、射频芯片等领域将 发挥重要作用。
Res BW、VID BW、 RBW
Res BW指的是分辨带宽, VID BW指的是视频带宽, RBW指的是实时带宽。
信噪比、动态范围、 相位噪声
这些参数描述了频谱分析 仪的性能,包括信号与噪 声的比例、动态范围以及 相位噪声水平。
四、频谱分析仪的典型应用
无线电通信
频谱分析仪用于无 线电通信系统的频 谱监测、无线电干 扰分析等应用。
《频谱分析仪讲》PPT课 件
#ห้องสมุดไป่ตู้频谱分析仪讲
一、频谱分析仪的基本概念
频谱分析仪的定义
频谱分析仪是一种测量电信号频谱分布的仪器,用于分析信号的幅度和频率特性。

频谱分析仪相位噪声测量原理27页PPT

频谱分析仪相位噪声测量原理27页PPT
频谱分析仪相位噪声测量原理
56、死去何所道,托体同山阿。 57、春秋多佳日,登高赋新诗。 58、种豆南山下,草盛豆苗稀。晨兴 理荒秽 ,带月 荷锄归 。道狭 草木长 ,夕露 沾我衣 。衣沾 不足惜 ,但使 愿无违 。 59、相见无杂言,但道桑麻长。 60、迢迢新秋夕,亭亭月将圆。
16、业余生活要有意义,不要越轨。——华盛顿 17、一个人即使已登上顶峰,也仍要自强不息。——罗素·贝克 18、最大的挑战和突破在于用人,而用人最大的突破在于信任人。——马云 19、自己活着,就是为了使别人过得更美好。——雷锋 20、要掌握书,莫被书掌握;要为生而读,莫为读而生。——布尔沃
Hale Waihona Puke END

最新-频谱分析仪原理.ppt

最新-频谱分析仪原理.ppt

-115 dBm (1 kHz BW & 0 dB ATTENUATION)
频谱仪平均噪声电平
安捷伦 N9000A 新产品&应用介绍
安捷伦N9000A CXA 信号分析仪
最新X系列信号分析仪提供了优异的性能, 已经收到广泛认可的用户界面,快速的测量 速度,丰富的测量功能,和优秀的扩展性.
节约成本, 提高测量速度 灵活配置 丰富的测量应用功能 矢量信号分析软件
显示的本底噪声电平依赖于RF衰减器
衰减器设值大 噪声电平高
显示的本底噪声电平依赖于RBW带宽
噪声电平随RBW 按
RBW1
10log----------
RBW2 规律变化
频谱仪最低本底噪声显示的设置
最小RBW设值 最小衰减器设值 减少VBW*(平滑谱线) 前置放大器(增益>噪声系数)
…更多功能,值得期待! 良好的使用性和代码兼容性
CXA Front Panel
Page 49
Introducing the New Low-cost CXA Signal Analyzer 2019/9/3
CXA Rear Panel
Page 50
Introducing the New Low-cost CXA Signal Analyzer 2019/9/3
(Normal) – 平均检波 – 准峰值检波
常用检波器的选择
1.测量CW信号,正峰值(Positive Peak) 检波器 2.测量噪声或者宽带信号功率,平均(Average) 或者 样本 (Sample)检波器 3.同时测量CW信号并观察噪声特性,标准正态(Normal )检波器
检波器与踪迹方式的关系
Page 57

噪声测量PPT课件优选全文

噪声测量PPT课件优选全文
衰减选择旋钮一般分上下两层,下层控制输入 衰减器,上层控制输出衰减器,每一档的衰减 量为10dB。使用时,应尽量将上层输出衰减器 旋钮沿顺时针旋到底,使输出衰减最大。只有 当信号微弱时,下层输入衰减调至最小时表头 指针仍偏转很小,才可减小输出衰减量。
注:声级计测得的噪声级分贝数,等于衰减器旋钮指示值 与表头指示值之和。
一般声:许多不同幅度、频率和相位的
正弦纯音的复合。包括噪声和乐声。
2024/11/20
有关噪声的声学知识
基本概念
乐声:较有规律 的振动所产生的周 期性的声波组合而 成的。 噪声(物理学定 义):无规则、非 周期性的杂乱声波。 噪声(心理学定 义):一切“不需 要的声音”。
2024/11/20
有关噪声的声学知识
LW
10lg W W0
式中 W——对应的声功率,W; W0——基准声功率,W0=10-12W。
2024/11/20
响度级和噪声级
1、响度级
响度:响度的单位为“宋”(sone),定义频 率为1000Hz的纯音,当声压级为40dB时的响 度为1宋;并规定声压级每升高10dB,响度则 增加1倍。 响度级:其单位为“方”(phon)。即选取 1000HZ的纯音作为基准声,若某声音听起来与 该纯音一样响时,则该声音的响度级(phon值) 就等于这个纯音声压级的数值(dB)。
2024/11/20
又称为国际标准
响度级和噪声级 等响曲线
纯 音 的 等 响 度 曲 线
2024/11/20
响度级和噪声级
响度级记作 LN,响度记作N,两者关系如下:
N 2 0.1LN 40
LN 4010log2 N 40 33.22lg N 从等响曲线可知:人耳的听感特性对高频声敏 感,对低频声迟钝。在4000HZ左右最敏感; 同一响度级的声音,频率越低,所需声压级越 高;响度级越高,曲线越平坦,即频率的影响 越小。

频谱分析仪相位噪声测量原理

频谱分析仪相位噪声测量原理

频谱分析仪相位噪声测量原理
1.直接法
直接法是通过频谱仪根据输入信号和参考信号之间的差异进行相位噪声的测量。

这种方法采用两个互补的技术:相干测量和非相干测量。

相干测量要求输入信号和参考信号在频率和相位上是一致的。

频谱分析仪会产生一个与输入信号相干的参考信号,并与输入信号进行运算,计算两者之间的相位差。

通过这种方法可以获得高精度的相位噪声测量结果。

2.自相关法
自相关法是通过频谱分析仪的自相关功能进行相位噪声的测量。

自相关是一种将输入信号与其自身进行运算的方法,用于计算信号的相关性。

频谱分析仪中的相关计算功能可以用于估计输入信号的相位噪声水平。

该方法的优点是简单易用,且可用于各种类型的信号。

相位噪声测量的基本步骤如下:
1.选择合适的测量方法和仪器设置。

2.提供输入信号。

输入信号可以是任何具有频率稳定性的信号源,例如射频信号源、时钟源等。

信号源应该尽可能干净,以避免噪声对测量结果的干扰。

3.相位噪声测量仪器设置。

根据输入信号的要求,设置频谱分析仪的中心频率、带宽、功率范围等参数。

4.执行相位噪声测量。

根据所选的测量方法,进行相干测量或非相干测量,或直接进行自相关计算。

测量过程中需要考虑到信号源的稳定性、测量仪器的灵敏度和噪声等因素,以确保测量结果的准确性。

5. 数据分析和结果评估。

根据测量结果,进行数据分析和结果评估。

相位噪声的评估通常使用相位噪声密度(PM Noise Density)和相关参数(例如RMS相位偏移、频率抖动等)进行表示。

噪声的测量PPT课件

噪声的测量PPT课件
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5 功能区噪声 (1)布点 功能区噪声监测,应选取代表性的测点,
进行长期监测。测点的选择,交通干线道路两侧 两点,其余功能区各设一点,多设不限,但一般 不少于六个。 (2)测量 测量时应选在无雨、无雪的天气,风速 小于4级,声级计安装在三角架上,传声器离地面 高度≥1.2m,距最近的反射体1m以上,传声器指 向较大的声源或垂直向上,带风罩,选用A计权快 档。
白天一般选在上午8:00—12:00,下午2:00—6:00.夜间一般 选在22:00—5:00
3 测量气象条件选择
测量气象条件一般为无雨、无雪天气,风力小于4 级(风速小于5.5m/s)。
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4 噪声干扰因素消除
传声器位置要准确,指向要对准检测方向,带 风罩。同时要保证仪器供电,仪器使用前后均应 校准,监测时间避免近距离人为噪声干扰。24h监 测应注意传声器防潮。 5 数据处理 6 评价方法
项目名称 区域环境噪声
道路交通噪声 厂界噪声 功能区噪声 扰民噪声 建筑施工厂界 噪声 机动车辆噪声
监测时间 白天上午8:00—12:00,下午2:00—6:00.夜间一般选在22: 00—5:00 白天正常工作时间内 工业企业的正常工作时间内进行,分昼间和夜间两部分 24h,每小时测量20min,或24h全时段监测 白天6:00—22:00,夜间一般选在22:00—6:00 在各种施工机械正产运行时间内进行,分昼间和夜间两部分
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个人观点供参考,欢迎讨论!
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(3)数据处理 噪声测量结果一般用统计噪声级或等效连续A
声级进行处理,即测定数据按公式计算出L10、 L50、L90、Leq和标准偏差s数值,确定城市区域 环境噪声污染情况。如果测量数据符合正态分布, 则可用下述两个近似公式来计算Leq和s:
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成都信息工程学院
微波测量技术
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频谱仪测量相位噪声的误差源
2. 频谱分析仪的线性误差 3. 参考电平设置的不确定误差(如果测量过程中参考电平
有调整) 4. 衰减器切换不确度(如果测量过程中衰减器有调整) 5. 频率响应误差(频率偏移大于 100 kHz) 5. 带宽的不确定性 (因为计算单位为 dBc/Hz)
dBc/Hz
噪声边带
动态范围 受限于 压缩/噪声
显示平均噪声电平
100 kHz to 1 MHz
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成都信息工程学院
微波测量技术
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雷达应用 – 指示运动目标
高的相位噪声引起目标判断混淆 目标反射信号
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频谱分析仪测量方法
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成都信息工程学院
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相位噪声测量结果
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成都信息工程学院
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相位噪声测量
• 相位噪声是描述信号质量的重要指标
• 单边带相位噪声(SSB)
• 是指相对于载波一定频偏处的1Hz带宽内的能量与 载波电平的比值,相应的单位为dBc/Hz
LC
1Hz
LPN
fo
foff
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成都信息工程学院
微波测量技术
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成都信息工程学院
微波测量技术
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谢谢大家!
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成都信息工程学院
感谢亲观看此幻灯片,此课件部分内容来源于网络, 如有侵权请及时联系我们删除,谢谢配合!
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微波测量技术
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剩余噪声的计算
相位噪声显示的是单边带噪声密度 L(f): S( f ) 是相位波动的频谱密度
dBc/Hz -> W/Hz:
剩余调相
rms
f2
2 Pnorm( f )df f1
剩余调频
f2
DFrms 2 f 2Pnorm( f )df f1
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频谱分析仪法的缺点与局限性
由于1Hz FFT滤波器形状带来的载波泄漏
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成都信息工程学院
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频谱仪测量相位噪声的误差源
1. 当测量结果和频谱分析仪的固有指标可以相比拟时,校正 频谱分析仪相位噪声带来的影响 。
举例: 如果测量结果比固有指标 高3dB,那么,测量的相 位噪声应该修正3dB。
抖动
jitterrms
rms
2fo s c
.
L(
f
)
1
0
lo
g10
S ( 2
f
)
L( f )
Pnorm( f ) 10 10
成都信息工程学院
微波测量技术
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频谱分析仪法的优点
测试设置简单、快捷 频率偏移范围大 (高达 1 GHz) 可以测试很多信号源的特性
杂散发射 邻信道功率泄漏 高次谐波
微波测量技术
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噪声边带对整机性能的影响
✓测量频率的下限 ✓频率分辨率 ✓灵敏度 ✓动态范围 ✓被测信号的相噪
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成都信息工程学院
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单边带相位噪声
phase noise / dBc/(1 Hz)
-70 -80 -90 -100 -110 -120 -130 -140 -150 -160 -170
直接显示相位噪声(当调幅噪声忽略不计时)
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成都信息工程学院
微波测量技术
பைடு நூலகம்
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频谱分析仪法的缺点与局限
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成都信息工程学院
微波测量技术
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频谱仪模式的不足和局限性
无法区分调幅噪声和相位噪声 灵敏度受仪器固有的相位噪声限制
无载波抑制 小频偏时测量范围受分辨率带宽和滤波器选择性所
限制
动态范围有限
从统计上而言是随机无线噪声,其特点是其通信信道上
的信号分布在很宽的频带范围内。
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成都信息工程学院
微波测量技术
相位噪声
• 一纯净的正弦信号可表达为: V(t)=Vssin2πf0t
• 由于噪声的存在,该信号的相 位是随时间随机变化的,因此 该信号可表达为
• V(t)=Vssin[2πf0t+Φ(t)]
Dcorr: RMS-检波器 (VBW > 3 ·RBW, 无平均):
Dcorr = 0 dB
取样检波器 (VBW < RBW):
Dcorr = 2.5 dB
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成都信息工程学院
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频谱分析仪法
参考信号
D 95.78 dB
频率偏移 300 kHz
.
显示300kHz频率偏移的相 位噪声-130.72 dBc/Hz = D – 10 * log RBW
其中Φ(t)是随时间而变的相位起伏, 也就是相位噪声
.
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微波测量技术
4
噪声边带
表示频谱分析仪本振短期不稳定度。
混频过程将任何本振不稳定性变换为混频分量。
噪声边带常用dBc/Hz表示(相对载频1Hz带宽内 的功率)。噪声边带又称相位噪声。
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成都信息工程学院
FSIQ7 (spec)
0.1
1
10
.
specification
typical
100
1000
10000
carrier offset /kHz
成都信息工程学院
微波测量技术
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噪声边带
相位噪声
噪声边带降低对不等幅信号的分辨率
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动态范围
动态范围依赖于到载波的间距
动态范围 受限于噪声边带
微波测量技术
1
相位噪声测量
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成都信息工程学院
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噪声
• 白噪声(white noise)
• 是指功率谱密度在整个频域内均匀分布的噪声。 所有频 率具有相同能量的随机噪声
• 高斯白噪声(WGN)
• 高斯白噪声的概念."白"指功率谱恒定;高斯指幅度取各 种值时的概率p (x)是高斯函数.
• 加性高斯白噪声(AWGN )
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直接频谱分析
1. 测量载波功率 P0 2. 测量某一频偏 fm 处的噪声功率
3. 结果:
L (fm )P 0 (P n o ,fm i s1 el0 oB H n go)( izs D k eo )rr
P0: 载波功率
Pnoise,fm: 频偏 fm 处的噪声功率
Bnoise: 分辨率滤波器噪声带宽
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