ii List Of Figures: Figure 1.1 multitone test principle .................................................................................... 7 Figure 1.2 Example of 7 frequencies multitone on time and frequency domain. ............. 8 Figure 1.3 Audio testing with multitone .......................................................................... 8 Figure 2.1 Single tone test ............................................................................................... 10 Figure 2.2 two tone test ................................................................................................... 11 Figure 2.3 multitone test for band bas filter.................................................................... 12 Figure 3.1 Test for linear device with single tone and how it act ..................................... 14 Figure 3.2 Test for non linear behavior device with single tone and how it act .............. 15 Figure 3.3 the behavior of single tone used to test amplifier in linear region ................ 15 Figure 3.4 the act of single tone use to test amplifier in non linear region .................... 16 Figure 3.5 the intermodulation distortion which appear in tow tone testing ................ 18 Figure 3.6 Themultitone output in time domain when constant initial phase used in all tones ........................................................................................................................................... 19 Figure 3.7 Themultitone output in time domain when random initial phase used in all tones ........................................................................................................................................... 20 Figure 3.8 A multitone signal in time and frequency domain ......................................... 21 Figure 3.9 the five measurements obtained from audio testing ..................................... 22 Figure 3.10 the appearance of one tone in time and frequency domain ....................... 26 Figure 3.11The frequency response of 13 different frequencies using single tone test . 26 Figure 4.1 Multitone signal with high crest factor ........................................................... 30 Figure 4.2 Multitone signal with low crest factor .......................................................... 30 Figure 4.3 generation of multi tone signal in matlab. The number of tones used 4 with the highest tone frequency is 10 MHz .................................................................................... 31 Figure 4.4 time domain representation of multitone signal with 32 tones ................... 32 Figure 4.5 multi-tone signal with random phase noise. ................................................. 33 Figure 4.6 Magnitude spectrum of the output of the parallel RLC circuit when test with 4 tones. ........................................................................................................................................... 34 Figure 4.7 Magnitude spectrum of the output of the parallel RLC circuit when test with 32 tones. ................................................................................................................................ 35 Figure 4.8 Circuit under test with defects tested with 32 multi-tone test signal. .......... 36 Figure 5.1 Series Tuned Colpitts VCO (Clapp VCO)……………………………….…38 Figure 5.2 the VCO circuit connected in white board………………………………..…39 Figure 5.3 BPF (RLC parallel circuit ) ………………………………………...………40 Figure 5.4 part (a) parallel RLC output with C= 2.2 μF part (b) same filter but di...….41 Figure 5.5 RLC series BPF output shape ……………..…………………………….…41 Figure 5.6 multitone signal in time domain……………………………………..…….44 Figure 5.7 multitone signal using the DSP kit and picoscope in time domain ………..45 Figure 5.8 multitone spectrum before testing the filter………………………………..45 Figure 5.9 Testing the BPF using the DSP kit……………………………………….…46 Figure 5.10 show the spectrum after testing the BPF using picoscpe……………..…...47 Figure 5.11 the spectrum of BPF after the test…………………………………………47 Figure 5.12 spectrum of BPF when changed the value of capacitor…….………….….48 Figure 5.13 spectrum of BPF when changed the value of capacitor……….……..……49 iii Abstract Multitone testing represent an advanced technique used for testing electronic devices whether it can be passive devices like filters or active like amplifiers and diodes, accordingly this test done for linear and nonlinear behavior devices, so in this report we aim to apply this test to linear device like band bass filter (BBF). Multitone testing considered as a sophisticated method because of the number of tones used to test device under test (DUT) more greater than traditional technique like single tone and two tone testing. This test stand for an operation of generating multitone signals consist of a summation of sine waves connected to the DUT which are connected to spectrum analyzer to obtain the frequency response and analyze it for the tested device,if it satisfied the determined specification needed ,then we decide to accept this device or neglect it by calculating a crest factor (CF) which give us an important indication about our judge and this practicability one of many applications of multitone testing. Moreover, this test considered as a practical mechanism done in manufacturing of electronic devices before product launch in the market to make sure the product meets the specifications that labeled to this item. • Chapter1 • Introduction • Overview Modern appetites for increased information from wireless devices has driven the complexity of communications modulation formats, as well as the complexity of the signal sources needed to test those communications systems. Advanced modulation formats often cannot tolerate linearity shortcomings of components in those systems, often visible as unwanted intermodulation distortion (IMD). Testing active and some passive components for susceptibility to IMD usually requires multitone test signals. While securing a rack of laboratorygrade signal generators can be expensive, multitone test signals can be generated cost effectively. Doing so requires a proper review of an application’s requirements and assembling a multitone test source that is flexible, practical, and accurate. This principle of using multitone signal allows acquiring the result of several measurement functions at different frequencies in a single step only. At the case of single tone and two tone testing represent a traditional technique for testing devices, these test no longer appropriate because it take longer time to achieve the test by forcing us to change the input frequency of the signal generator each time, furthermore these test have less accuracy of it results since it depends on one or two tone as a maximum case to check the frequency response output appears on the spectrum analyzer. Nowadays because of the enormous development in communication and the huge demand of electronic devices in all over the world the previous technique down and anew one arises in the environment of the communication meet the spread of advanced manufacturing of electronic products through the productivity stages called multitonetesting which stand for a powerful approach is the use of a multitone signal as stimulus. This principle allows to acquire the result of several measurement functions at different frequencies in a single step only, although this mechanism aims to overcome the time bottleneck. It bases on the principle of simultaneously transmitting all the sinusoidal tones -frequencies- of interest in a single burst. This stimulus is called ‘multitone signal’. In a typical multitone measurement, the generator sends the user defined burst through the DUT to the analyzer as in . Figure 1 1.1 multitone test principle Figure 2 shows two pictures represent a multitone signal with 7 frequencies, displayed on an oscilloscope in the time domain and on a spectrum analyzer in the frequency domain respectively: Figure 2 1.2 Example of 7 frequencies multitone on time and frequency domain Also multitone used in most audio test instruments stimulate the device under test (DUT) with a single sinusoidal wave. By analyzing its output signal, one test result per frequency - e.g. Distortion or Noise - may be acquired. Another, more powerful approach is the use of a multitone signal as stimulus. This principle allows to acquire the result of several measurement functions at different frequencies in a single step only. Figure 3 shows how multitone testing used in audio: Figure 3 1.3 Audio testing with multitone • Existing Problems • The key problems that necessitate carrying out this project can be summarized as follows:. Solving the time and cost issue by finding a way that used for generating a multitone signals unlike traditional test which need a lot of time to achieve. • Finding a way for characterizing the linear and non linear behavior to solve the intermodulation distortion and the harmonics. • Writing an efficient code using matlab could be able to detect if the device is faulted or not. • Knowing the characteristic of the channel that the multitone signal transmitted then passing throw a channel to test the device under test (DUT). • Motivation for Carrying out the Research The main objectives of our project and report are to gain experience in team working and to practice many aspects of Scientific Research, Web Search and Technical Writing.learn how to deal with problems you faced during the work and try to use the knowledge we get in practical way to release the different between the theory and the application. Learn newer methods that are used in producing companies to examine the electronic devices and try to find a new way to apply this test with short period of time to test device ,also this way has less cost due to other traditional techniques. • Chapter 2 • Methods used to test DUT • • 2.1 Single tone measurement This test is simple since it depends on one signal need to test DUT and then characterizing the out of spectrum analyzer figure 4 demonstrate this test: Figure 4 2.1 Single tone test The most striking advantage of single-tone measurements is simplicity: • It allows the performance of a DUT to be evaluated over a range of frequencies with a single tone measurement. • The characteristics of a multitone waveform (e.g., spectral content, crest factor, etc.) give it a much closer resemblance to typical audio program material like music or speech, than a single sine wave. • • 2.2 Two tone test (measurements): Similar to single tone test but we use tow tones to get the output as shown on figure 5. Figure 5 2.2 two tone test This test usually used for third-order intermodulation distortion (IMD3) which represent the measure of the third-order distortion products produced by a nonlinear device when two tones closely spaced in frequency are fed into its input. This distortion product is usually so close to the carrier that it is almost impossible to filter out and can cause interference in multichannel communications equipment.IMD is measured by examining the output of a device under test (DUT) with a spectrum analyzer while the DUT is being stimulated with a two tone test signal, when characterizing the nonlinear behavior of an amplifier. Two discrete tones with equal power, that fall within the pass band of the DUT, are applied to the input of the DUT as in figure 5. The resultant harmonic and intermodulation distortion products are then measured using a spectrum analyzer. • 2.3 Multitone test: This represent an advanced test which could be more complicated compared with the previous tests. For example if we want to generate a multitone signal (200 sine waves combined to each other in the conventional test mentioned before this idea has one meaning that we need 200 signal generators to generate multitone signal and this action requires a lot of money and time. In this project the signal generator which give us the multitone replaced by constructing a code in matlab meets our requirement of getting the multitone signals. In this project the multitone signal represents the test stimulus for the device under test DUT. The DUT parameters are extracted by using a spectrum analyzer from the DUT output, we can compute the crest factor. The crest factor can be considered as a good indicator to decide if the DUT meets the desired specifications or not. Figure 6 demonstrate the terminology of what we conduct in this project: Figure 6 2.3 multitone test for band bas filter • • 2.4 Advantages of multitone test The basic principle of saving time and money through using multitone testing mechanism is to compare it with the conventional tests used to done before .In the traditional methods like single and two tone measurement to conduct a test for any device this operation takes a lot of time since at these test we must have at least one signal generator at the case of single tone and every time we need to wait for the first frequency generated then analyze the frequency response output whole this process done for the first frequency generated but these test depends in using several frequency so we need to generate a new frequency then repeats the complete steps for several times . In tow tone testing measurement we need two signal generators connected to the tested device to obtain the output, similarly the same problem still stand that we need to change the input frequency of generator every step. If we want make the test faster by generating more than one frequency in one step this mean we need a large number of signal generators each one tuned with different frequency than others with a combiner all connected to DUT and this technique if it is actually reduced the time but increase the price of achieving this test and it needs a huge budget. On the other hand , in multitone approach we can generate multitone signal simply by writing a code in matlab this operation represent the multitone signal itself and apply this code for the tested device to get the frequency response output which we could analyze it by using matlab, the result we obtain from this test doesn’t take a lot of time , and this meets the requirements needed in the global factories which specialize of producing electrical devices with its variety in all applications since multitone testing represent an advance technique achieve three important factors in a consecutive way accuracy ,speed in taking result , low cost technique. • • Chapter 3 • Application of multitone testing • 3.1 Testing linear and non linear devices like band pass filter, amplifier….etc. We decide in this project to work on testing linear device using multitone signal to conduct this test well as possible. Therefore we should gain a good understand of linear and non linear behavior concepts of the tested device. Devices that behave linearly only impose magnitude and phase changes on input signals. Any sinusoid appearing at the input will also appear at the output at the same frequency. No new signals are created. When a single sinusoid is passed through a linear network, we don't consider amplitude and phase changes as distortion. However, when a complex, time-varying signal is passed through a linear network, the amplitude and phase shifts can dramatically distort the time-domain waveform. Figure 7 shows how single sinusoidal act through a device has a linear action : Figure 73.1 Test for linear device with single tone and how it act Unlike linear behavior, non-linear devices can shift input signals in frequency (a mixer for example) and create new signals in the form of harmonics or inter-modulation products. Many components that behave linearly under most signal conditions can exhibit nonlinear behavior if driven with a large enough input signal. This is true for both passive devices such as filters and even connectors, and active devices like amplifiers. Figure 8 shows the effect of nonlinear behavior . Figure 83.2 Test for non linear behavior device with single tone and how it act To understanding the matter of distortion in both cases of devices behavior we enter a single sinusoidal cosine wave through an amplifier. In linear region only the amplitude increased as seen in figure 9. Figure 9 3.3 the behavior of single tone used to test amplifier in linear region On the other hand, the intermodulation harmonics clearly appears when the amplifier received an input, the most critical out-of-band distortion is typically the 2nd order and 3rd order distortion. If we develop the 2nd order and 3rd order terms in the Malaren series for a single tone input, we obtain distortion terms at the multiples of the fundamental frequency. These correspond to the 2 nd order and 3rd order harmonics .Harmonic distortion is typically specified relative to the fundamental level. If the fundamental power level changes by a certain amount in dB, the power level of 2nd and 3rd order harmonics changes by twice or three times the same amount in dB, respectively. For example, for a 1 dB increase in the fundamental results in a 2 dB increase of the 2nd harmonic and in a 3 dB increase of the 3rd harmonic. This means that the relative level of the 2nd harmonic to the fundamental will be 1 dB larger than it was, and the relative level of the 3rd harmonic will be 2 dB larger. Therefore, when specifying the relative or absolute level of the 2nd harmonic distortion, for example, it is imperative to also specify the level of the fundamental at which the distortion was measured. Once this is provided, the 2 nd harmonic distortion can be theoretically predicted for any power level at the fundamental. However, this prediction only holds true for the more linear section of the power transfer function of the device, so it can only model distortion in devices under small signal excitation, from figure 10 we can see the harmonic distortion represent in nonlinear region. Figure 10 3.4 the act of single tone use to test amplifier in non linear region Now we will see if more than one frequency enters to amplifier at the case of non linear region. The two-tone continuous wave distortion measurement is the most common test used to characterized the 3rd order IMD in a device .also two-tone signals are used extensively in the communications industry to test for nonlinear distortion at the component, device, sub-system, and system level. Intermodulation distortion -IMD- is a particular type of nonlinear distortion; other types include harmonic distortion and cross modulation. IMD is the primary cause of in-band and out-of-band spectral regrowth (i.e. distortion) and results from unwanted intermodulation between the multiple frequency components that comprise a signal. Intermodulation occurs as a result of the signal traversing components and devices with nonlinear transfer functions. Intermodulation (IMD) is the formation of combination frequencies resulting from a nonlinear transfer characteristic when the input signal comprises several frequencies. The 3 rd order intermodulation products are typically the most problematic, since their frequencies are relatively close to the fundamental frequencies. As with any 3 rd order distortion, when the power level of the fundamental increases by a certain amount in dB, the power level in dB of the IMD will increase by three times that same amount in dB, or its relative level to the fundamental will increase by twice that amount in dB. Therefore, when specifying the relative or absolute level of 3rd order IMD, the level of the fundamental must also be specified. Once this is provided, the 3rd order IMD can also be theoretically predicted for any power level at the fundamental. Figure 11 shows the intermodulation distortion which occur for non linear device like amplifier using two tone measurement and shows the IMD products generated when two tones at frequencies f1 and f2 are presented to the input of a nonlinear device. Figure 11 3.5 the intermodulation distortion which appear in tow tone testing It is obvious that tow tone measurement represent a strong technique for characterizing inter modulation distortion, because of that nonlinear behavior is important to quantify, as it can cause severe signal distortion. Common nonlinear measurements include harmonic and intermodulation distortion (usually measured with spectrum analyzers and signal sources). IMD is measured by examining the output of the device under test (DUT) with a spectrum analyzerwhile the DUT is being stimulated with a multitone test signal. Multi tone signals also affected by the relationship of the phase of each tone, so considering the phase of multitone is zero or adding phase to these signal directly affect the peak value of the output signal and the average value which directly affect the crest factor .also affect the IMD measured at a specific frequency varies widely depending on the phase relationships of the tones that comprise the test signal. So when summing multiple frequencies, the phase relationships of the frequency components affect the time-domain profile and peak-to-average characteristics of the composite signal. Figure 12 shows the composite signal when all the tones have the same initial phase : Figure 12 3.6 Themultitone output in time domain when constant initial phase used in all tones Figure13 shows the composite signal when the tones have a random initial phase setting. Although IMD is noticeably dependent of the phase relationships of the tones, IMD Test results from one phase set are not predictive of IMD test results from another phase Set based on phase relationships of the tones or peak-to-average ratio of the composite Signal; in other words, IMD test results are not strongly correlated to the phase relationships of the tones in a statistical sense. Consequently, as the phase relationships of the spectral components in the pass band of the DUT vary over time, the nonlinear distortion characteristics of the DUT vary in an unpredictable manner. As a result, testing with a single phase set does not provide enough information to adequately characterize IMD. Figure 13 3.7 The multitone output in time domain when random initial phase used in all tones • • 3.2 Audio testing The trend in modern audio testing is to reduce more and more the time required for complete performance test of the device being tested. This tendency results partly from the demand of broadcasters being forced to provide 24hour programming, leaving little time for testing. Most audio signal measurements are performed by stimulating the device to be tested with a test signal and analyzing the transmitted signal as soon as it has passed the device. One must be aware that the result of this evaluation consists of a few core quantities only, all of them relating to the capabilities of the human hearing sense. More advanced tests such as intermodulation distortion measurements stimulate the device with a pair of sinusoidal signals to come closer to the real situation of audio signal transmission. In the presence of nonlinear transfer characteristics, the DUT generates new harmonic and intermodulation frequencies. However, in practice the device is normally stimulated by music or speech which is a far More complex signal than any single or twin tone test. Many frequencies with non-correlated phase relations exist in such a real-world signal. Therefore, multitone testing is a much more realistic approach for audio testing, emulating the complex structure of natural sound. A multitone signal typically contains 2 to ~31 signal frequencies, each with a certain phase relation, distributed over the frequency band of interest. Obviously, sophisticated test instruments are necessary to analyze all these signals with their interactions on each other. Figure 14shows a typical multitone signal in the time- and frequency domain: Figure 14 3.8 A multitone signal in time and frequency domain Obviously, it is necessary to characterize the time signal by an appropriate value in order to allow the optimization of its phase relations. The most suitable measure for this purpose is the Crest Factor (CF), which is defined as For any multitone signal with given RMS value, the Crest factor will change with the peak value, which in turn depends on the phases of the signal components. An optimal distribution of the phases results in a low peak value of the resulting time signal and therefore a low Crest factor will occur. Alternatively, the principle of a multitone test, providing five measurement results, all acquired in parallel at a time, may be described by following picture in fig 15. Figure 15 3.9 the five measurements obtained from audio testing These five measurements are: • Level: it indicates the complete energy content of the test signal. • Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency. • Distortion: Both the Harmonic Distortion (THD+N or SINAD) and Intermodulation Distortion test refer to new signal components or frequencies that are generated by the DUT. The Total Harmonic Distortion (THD) is defined as the ratio between the power of the harmonic frequencies above the base frequency and the power of the base frequency. This ratio is displayed in dB's. It is a measure of the distortion in a signal. The THD is calculated using the follow In formula: Where: V1 is the signal amplitude in rms voltage V2 is the second harmonic amplitude in rms voltage Vn is the nth harmonic amplitude in rms voltage SINAD: Signal to Noise and Distortion Ratio is a parameter which provides a quantitative measurement of the quality of an audio signal from a communication device. For the purpose of this article the device is a radio receiver. The definition of SINAD is very simple - it’s the ratio of the total signal power level (wanted Signal+ Noise + Distortion or SND) to unwanted signal power (Noise + Distortion or ND). • Noise :Noise measurement is normally done with a quasi-peak detector • Crosstalk : notice when characterizing non linear behavior especially the 3 rd harmonic distortion since it very close the fundamental frequency In order to understand the multitone testing process and audio testing in special case, it is vital to understand some basics of signal generation and especially the meaning of the following concepts: • Bins & Signal Bins First, a discretely generated time signal of blocklength, i.e. the number of samples which build the signal, as well as the sampling frequency fs. The following equation shows how we calculate the possible frequencies of a time signal limited length can comprise certain frequencies only. These frequencies fn is given by the Where: fs: the sampling frequency n : integer number Blocklenght: the number of samples that are actually used for one FFT fn : the possible frequencies of a time signal. These possible frequencies have been named bins. However, a practical Multitone signal will almost never comprise all possible frequencies, but a user-defined selection of them only. These actually set bins are called signal bins. Furthermore, the bins and signal bins are normally not described by their frequencies, expressed in Hertz, but instead by their bin number. This value is obtained by numbering all possible frequencies starting with the lowest possible value. Alternatively, the bin numbers can be calculated according to: • Bandwidth The available frequency range of the transmission path always has to be considered. It is defined by the minimum and maximum frequency which can pass through the DUT. • Number of Samples The analysis of every audio parameter has to be optimized by the appropriate choice of the test signals. For instance, a detailed frequency response requires more frequencies to be measured than a crosstalk test, where few frequencies needed. • Number of Signal Bins The question about the optimum number of signal bins to be set for a certain test depends on several parameter. • In most industrial applications, it is necessary to check a few 3 to 5 selected core frequencies only. Usually, this already allows a Good / No-Good decision, providing enough security that all faulty samples are found. • From another point of view, one may take into account the specific demands of the different measurement functions. The level and phase measurement may require a larger number of signal bins in order to get a precise representation of the frequency and phase response. On the other hand, the distortion, noise and crosstalk test should be restricted to a few signal bins only, resulting in more meaningful measurement values • Frequency Spacing The frequency spacing f corresponds to the lowest frequency that can be generated & analyzed. It defines the spectral resolution of the FFT and is calculated by following formula. On the other hand, practically single tone also used a sine signal with one specific frequency, the following graph for one sinusoidal signal fig 16. Figure 16 3.10 the appearance of one tone in time and frequency domain In order to get a characterization over the complete frequency range, the generated signal must be swept through the band of interest, i.e. its frequency has to be increased (or decreased) stepwise, while at every step a measurement is executed. For instance, the frequency response of a DUT in the audio range can be evaluated with a single tone test signal starting at 20Hz and ending at 20 kHz as shown in figure 17: Figure 17 3.11The frequency response of 13 different frequencies using single tone test • 3.3 Channel Estimation In wireless communication channel estimation refers to known channel properties of a communication link. This information describes how a signal propagates from the transmitter to the receiver and represents the effect which happened to the original signal, for example, scattering, fading, and power decay with distance. Channel estimation usually refers to estimation of the frequency (and potentially spatial) response of the path between the transmitter and receiver. This knowledge can be used to optimize performance and maximize the transmission rate. In this application the multitone signal represent the input signal transmitted from the transmitter through a channel could be a free space, coaxial cable or any medium until the signal picked up by the receiver. • Chapter 4 • Simulation • • 4.1 Crest factor The Crest Factor is equal to the peak amplitude of a waveform divided by the RMS value: Also Where: Cf: the crest factor VP: the peak voltage Vrms: the rms value. The purpose of the crest factor calculation is to give an analyst a quick idea of how much impacting is occurring in a waveform. When measuring a DUT with a test signal, we usually don't think about the peak value of the signal, it makes sense when we remember that the peak level of a sine wave equals approximately 1.41 times its RMS value. However, things are different when working with multitone signals that are put together by two or more sine waves with different frequencies. In such cases, the resulting time signal, which is obtained by adding its components, will show a much larger difference between its RMS and peak value. In order to allow the characterization of a signal, a relationship between its peak and its RMS level had to be established, the so-called Crest factor Cf. It indicates the ratio of the peak level of the signal to its RMS level. Consequently, a high Crest factor corresponds to a signal having a high peak voltage compared to the average signal level. Different multitone signals have different Crest factors, depending on the number of signal bins and the phase relations between them depend on the chosen phase relationship. Furthermore, it is vital to know that the higher the Crest factor of a multitone signal, the poorer the signal to noise ratio of the measurement. This can be explained easily when considering the shape of a multitone signal with a high Crest factor. As we see in figure 18, the peak value of the signal is far above its average (RMS) level. Obviously, when transmitting such a signal through a DUT, one must adapt the peak voltage of the signal to the max. Allowable voltage of the DUT in order to avoid clipping. Consequently, the RMS voltage of the signal becomes very small, thus coming closer to the noise floor of the transmitted signal. . Figure 18 4.1 Multitone signal with high crest factor So if we look to the same multitone signal, but this time with optimized phase relations between its signal bins, displayed in figure 19. This time, the difference between the peak voltage of the signal and its RMS level has become much smaller. This does not only reduce the necessary headroom for signal transmission, but also improves the signal-to-noise ratio by far. Figure 19 4.2 Multitone signal with low crest factor As a conclusion, the Crest Factor is a quick and useful calculation that gives the analyst an idea of how much impacting is occurring in a time waveform. • 4.2 Generation of multi-tone signal In this section, the multi-tone testing algorithm will be applied to a linear passive network. The linear passive network chosen to test the multi-tone stimulus is a parallel RLC circuit. For example if we use a multi-tone signal composed from four tones with the highest tone frequency is 10 MHz, then the resulting multi-tone signal appears as shown in : Figure 20 4.3 generation of multi tone signal in matlab. The number of tones used 4 with the highest tone frequency is 10 MHz The crest factor for the multi tone signal shown in is. If the number of tones is increased to 32 with the highest tone frequency of 10 MHz, then we can see the peak of the multi tone signal became larger and its period also became larger as shown , while the crest factor increases up to. Figure 21 4.4 time domain representation of multitone signal with 32 tones The above generation for the multi-tone signal assumes zero phase for the generated signal. Multitone signal with large crest factor is undesirable for applications with the nonlinearity. However the crest factor can be reduced by adding phase noise to multi-tone signal. This concept can be illustrated by re-simulating the previous 32 tones with random Gaussian noise added to the phase of each tone. The simulation result is shown in . A comparison between and shows that the peak amplitude of the multi-tone signal with random noise is much less than the peak amplitude of the signal. The crest factor of the multi-tone signal with phase noise is 2.81 compared with 5.33 for the multi-tone signal without phase noise. Figure 22 4.5 multi-tone signal with random phase noise. The number of tones is 32 similar to that shown in • • • • • • • • • 4.3 Testing the a linear circuit with multi-tone In this section, testing a parallel RLC circuit with the multi-tone signal will be used to demonstrate the concept of multi-tone test. The values of R, L and C where selected to model a band pass filter whose center frequency is and its bandwidth is. In particular the values of RLC are selected as, and the circuit is first tested with a multi-tone signal composed from four tones added with phase noise. The output of the circuit is analyzed with Fourier transform to show its frequency response. Figure 23 4.6 Magnitude spectrum of the output of the parallel RLC circuit when test with 4 tones. The magnitude spectrum of the signal detected at the output of the circuit under test is shown in . From , we can see that there spectrum of the tested circuit is centered about 5 MHz, but the bandwidth is not properly represented or clarified. If the number of tones is increased to 32 tones, then the resulting signal appears as shown in Figure . Figure 24 4.7 Magnitude spectrum of the output of the parallel RLC circuit when test with 32 tones. From , it is clear that the spectrum of the tested signal is properly identified. As a result to this discussion we can see that the as the number of tones is increased we can estimate the characteristics of the device under test properly. The crest factor measured at the output of the device under test (parallel RLC circuit) when it is excited by the 32 tones is. If we assume that the circuit under test is subjected to manufacturing defects, such that its center frequency is altered, then the crest factor will change as. The change in crest factor will indicate that the circuit under test is defected. To demonstrate this results assume that the inductor value is changed from the to. If the circuit under test is tested again with the 32 tones, then the resulting magnitude spectrum is shown Figure 25 4.8 Circuit under test with defects tested with 32 multi-tone test signal. We can see that the center frequency of the defected circuit is not 5 MHz also the crest factor is. If we compare the crest factor for the circuit with no defect with the defected circuit we can see a clear difference between them (almost 12.5%). Since analyzing the spectrum of the circuit under test each time the circuit needs to be tested will take long time for performing the analysis and comparison. The crest factor represents a faster testing method to determine whether the circuit under test is defected or not. This testing technique can save time with the number of devices to be tested is very large (approaching 1 million or larger). For this reason testing with multi-tone and crest factor analysis is recommended for large volume production. • • • • • Chapter 5 • Experimental work • 5.1 Building a VCO (voltage controlled oscillator ) In this chapter we aim to check if the results of theoretical and apply it in practical , by conducting tow experiment in order to generate the multione signal and use it to test RLC circuit make sure that our results will be matched by theoretical results ,accordingly these practical two experiments building a voltage controlled circuit (VCO) and generating the multitone using dsp kit in the DSP lap to prove that using multitone test to check the DUT is better than single tone and two tone and getting the results and analyze it ,this test can save time and give more accurate results and more than one measurement . Building a voltage control oscillator (VCO) circuit : The aim of building a VCO circuit to gain a good range of frequency in order to test the DUT by changing the input voltage which leads to change the output frequency . Basic oscillator design specifications often require a given output power into a specified load at the design frequency. The drive level and bias current set the fundamental output current and the oscillation frequency is set by the resonator components. Transistor selection of the transistor should consider noise, frequency, and power requirements. Based on the particular device, the design may account for parasitics of the device affecting resonator components as well as nonlinear performance specifications. To get a low phase noise we should Maximize the power at the output of the oscillator, Choose a varactor diode or any device could Meet the same purpose with a low equivalent noise resistance. We choose a Series Tuned Colpitts VCO (Clapp VCO) topology to be the circuit which we conducted in this project as shown below : Figure 26 5.1 Series Tuned Colpitts VCO (Clapp VCO) The series-tuned Colpitts circuit (or Clapp oscillator) works in much the same way as the parallel one. The capacitor, C1, is positioned so that it is well-protected from being swamped by the large values of C3 and C4. In fact, small values of C3, C4 would act to limit the tuning range. Fixed capacitance, C2, is often added across the varicap to allow the tuning range to be reduced to that required, without interfering with C3 and C4, which set the amplifier coupling. The series-tuned Colpitts has a reputation for better stability than the parallel-tuned original. Note how C3 and C4 swamp the capacitances of the amplifier in both versions. we apply the VCO circuit and connected in white board to get the desired range of frequency wanted as seen in the following graph : Figure 27 5.2 the VCO circuit connected in white board We found that our output range of frequency of the series tuned VCO obtained from the circuit which shown on the digital oscilloscope 19.34 MHz to 22.75 MHz which mean it can cover a range of frequency around 3.5 MHz . This range was not enough to test the BBF and the frequency was very high compared to DSP kit ,so we decide to use a frequency generator as a VCO to test the RLC circuit .In order to get the VCO principle and apply it on our circuit we need two function generators , we use one of them to get a ramp signal to the BBF and we will draw the changing in voltage when we change the frequency in a graph and we will see if we get exactly the shape of band bass filter or not . •5.2 Building a BPF (RLC parallel circuit ) At this stage we will build a band pass filter (RLC) to get these specifications: Band width = 4 KHz , cutoff frequency (Fc) = 10 KHz Accordingly the values of R,L and C calculated from these equations: And we find R = 1k Ω,L = 0.25μF, C=1mH Figure 28 5.3 BPF (RLC parallel circuit ) After we connect the RLC circuit we use it to be tested by the VCO which we build it to implementation the principle of single tone , and test by multitone using the DSP kit . Figure 29 5.4 part (a) parallel RLC output with C= 2.2 μF part (b) same filter but di we notice from figure 29 part (a) that we use the principle of single tone by using a function generator with ramp output to test the RLC parallel circuit and the output was typically a BPF with fc=12.33 kHz and the circuit has And we find R = 1k Ω,L = 0.25μF, C=1mH while part (b) same filter but we changed the value of C we can see that the output is defected ,also the center frequency changed in order to get the output correct which it is the shape of BPF we need to change the frequency from the function generator to get the correct BPF and this action take a lot of time due to manual calibrating. Figure 30 5.5 RLC series BPF output shape This graph show how could the output signal of series RLC circuit (BPF) which appears clearly . •5.3 Generating the multitone signal using DSP kit This principle of multitone allows to acquire the result of several measurement functions at different frequencies in a single step only, although this mechanism aims to overcome the time bottleneck . the multi-tone testing will be applied to a linear passive network. The linear passive network chosen to test the multi-tone stimulus is a parallel RLC circuit It bases on the principle of simultaneously transmitting all the sinusoidal tones -frequencies- of interest in a single burst. This stimulus is called ‘multitone signal’. The basic idea from both ways of test the BPF that we could get the results from the VCO circuit and the experiment which done on DSP kit after we analyze the both sources we calculate the Crest Factor (Cf) and the time duration to be able to judge which test is the best . In this experiment which done in the DSP lap using DSP kit and picoscope and a program code composer studio -CCstudio- and the procedure to generate the multitone to be able to test the band pass filter as the following: we convert the multitone code which was written in matlab to C language in order to deal with code composer studio to be able to download the code on the DSP kit and after that we will see the multitone before using the test on RLC circuit , we connect the picoscpe to see our tone and how much the bandwidth it covers, and the code needed as the following which used in composer studio to download it in DSP kit : include "dsk6713_aic23.h" //support file for codec,DSK# #include "multitone.h" Uint32 fs = DSK6713_AIC23_FREQ_96KHZ; //set sampling rate short loop = 0; //table index short gain = 10; //gain factor interrupt void c_int11() //interrupt service routine { short sample_data; output_sample(multitone[loop]); //output data if(++loop>128) loop=0; //reset the loop when all samples are sent to the output return; } void main() { comm_intr(); //init DSK, codec, McBSP while(1); //infinite loop } //end of main After that we take a vector contains many sample and represent the number of sample which we want to take in our consideration to get the multitone signal to be able to check the band bass filter . The vector could be like that : short multitone[]={ 212, 208, 102, 21, -10, ... … } This is multitone signal in time domain which we deal with without testing the RLC from matlab : Figure 31 5.6 multitone signal in time domain This is the multitone signal which we see from using the DSP kit and picoscope in time domain : Figure 32 5.7 multitone signal using the DSP kit and picoscope in time domain This one represent the multitone spectrum before testing the filter : Figure 33 5.8 multitone spectrum before testing the filter We notice that the multitone cover a range of 24 KHZ , so we will take in our design of our band pass filter . After that to see what happened when we connect the BPF , we take the output line of the dsp kit and connect it to the RLC circuit and and we get the spectrum result correct , scince it has exactly the shape of BPF . These pictures shows the component needed to apply this experiment : Figure 34 5.9 Testing the BPF using the DSP kit Experiment in DSP lap using DSP kit . Figure 35 5.10 show the spectrum after testing the BPF using picoscpe Experiment work using picoscpe to show the spectrum after testing the BPF . This picture shows the spectrum using BPF to be tested using the multitone principle: Figure 36 5.11 the spectrum of BPF after the test From this figure we find that the crest factor CF equal to 2.587 and this is the value which represented by using a band bass filter with these specifications R = 1k Ω,L = 0.25μF, C=1mH . It is noticed that the time to get the result in the principle of using multitone is in micro seconds . this mean that this test can save time when we concerned of big companies . As we said our judje to accept the device or not by calculating the crest factor so changing any one of R,L or C should give a difference values of crest factor as shown below : The spectrum of BPF using R = 1k Ω,C = 10pF, L=1mH : Figure 37 5.12 spectrum of BPF when changed the value of capacitor This lead to change the value if CF . The spectrum of BPF using R = 1k Ω,L = 100pF, L=1mH Figure 38 5.13 spectrum of BPF when changed the value of capacitor We notice that that changing any parameter of band pass filter lead to change the crest factor and this how companies which produce these devices use this principle to check their products before launch it to the market. •5.4 Results and conclusion We find that using the multitone teqnique and the crest factor to judge for the device to be accepted or not is an efficient way since any change in any parameters on the device lead to change the crest factor and this what we are looking for that this test can let us compare between any two devices easily and with a negligple time could reach to micro second . This mean this test can give and accurate results in less time due to compare with using a VCO and single tone principle which need more time and less in accuracy and hard to judge when comparing between any active or passive device . • • • • • • • • Chapter 6 • References [1]. KLIPPEL GmbH. http://www.klippel.de/measurements/nonlinear-distortion/multi-tonedistortion.html. KLIPPEL GmbH in Dresden/Germany. Oct. 2006 . [2]. Agilent Technologies. Two-tone and Multitone Personalities,Application Note 1410. USA : Agilent Technologies, February 6, 2003. [3]. Generation and Conditioning . USA : Agilent Technologies, December 2002. [4]. NTi Audio AG. Comparing Conventiona lvs. Multitone Testing,A2 . Rapid Test. Liechtenstein : NTi Audio AG, Mar. 2000. [5]. Alan V.Oppenheim, Ronald W.Schafer,Joun R.Buck. Discrete-Time Signal Processing . Upper saddle river,New Jersey : Prentice-Hall,Inc., 1999. [6]. NTI AG. Multitone Testing,RAPID-TEST Applications. FL-9494 Schaan,Liechtenstein : NTI AG, Mar. 2000. [7]. José Carlos Pedro, Nuno Borges Carvalho. Intermodulation Distortion in Microwave and Wireless Circuits. 2003. • Chapter 7 • Appendices %function[waveform]=mtpr_input(bin_start,bin_stop,sample_size,samp_freq,max_PAR) clear all clc %for z=1:100, clear x tic fcarrier = 10e6; A = 5; % Frequency of the RF carrier 1 GHz % The perak amplitude of the test signal sample_size=2^16; % Number of samples taken for simulation samp_freq=4*fcarrier; N_Tones=256; % bin_start=33; % bin_stop=256; % max_PAR=16; % missing=[48 72 96 120 144 168 192 216 240]; % Generating tone frequencies freq=(fcarrier/N_Tones)*(1:256); % m=0; % for k=1:N_Tones, % freq(k)=m+fcarrier/N_Tones; % m=freq(k); % num_tones(k)=k; % end %********************************************************************** %********************************************************************** %generation phases thetha(1:N_Tones)=0.6+sqrt(pi)*randn(1,N_Tones); %%%%%%%%%%%%%%%%%%%%%%%%%%%% %thetha(1:N_Tones)=0; %load('thetha.txt') %generatin amplitudes amp=ones(1,N_Tones); GAUSS_NOISE=0.2+sqrt(0.01)*randn(1,sample_size); %This statemnt generates a gaussian noise signal with 0.2 mean and 0.01 variance t=0; Ts=1/samp_freq; % Sampling interval x=zeros(1,sample_size); for i=1:sample_size, for j=1:N_Tones, x(i)=x(i)+amp(j)*sin(2*pi*t*freq(j)+thetha(j)); % samples taken from the 256 tones end % x(i)=x(i)+GAUSS_NOISE(i); % This statement adds a gaussian noise to the multitone signal carrier(i) = A*sin(2*pi*t*fcarrier); modu(i)=x(i)*carrier(i); multiplying the carrier by the multi tones time(i)=t; t=t+Ts; end freq_x=fftshift(fft(x)/sample_size); freq_carrier=fftshift(fft(carrier)/sample_size); freq_modu=fftshift(fft(modu)/sample_size); figure(1); subplot(3,2,1) % The equation for the signal under test % modu is the signal obtained from plot(linspace(0,Ts*sample_size,sample_size),x); title('Multitone signals with noise'); xlabel('time ns'); ylabel('Amplitude V'); subplot(3,2,2) plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(freq_x(1:sample_size))); title('Spectrum Multitone signals with noise'); xlabel('Freq GHz'); ylabel('Magnitude V'); subplot(3,2,3) plot(linspace(0,Ts*sample_size,sample_size),carrier); title('RF carrier'); xlabel('time ns'); ylabel('Amplitude V'); subplot(3,2,4); plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(freq_carrier(1:sample_size))); title('Spectrum carrier'); xlabel('Freq GHz'); ylabel('Magnitude V'); subplot(3,2,5) plot(linspace(0,Ts*sample_size,sample_size),modu); title('Carrier x dithered multitone'); xlabel('time ns'); ylabel('Amplitude V'); subplot(3,2,6); plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(modu(1:sample_size))); title('Spectrum carrier x dithered multitone'); xlabel('Freq GHz'); ylabel('Magnitude V'); modu=modu'; % plot(x); % % inputplot=Four(x,4e9); % %converting to db % inputplot.amp % figure(2); % plot(inputplot.frq(1:8:end),inputplot.amp(1:8:end)) % inputplot.amp=10*log10(inputplot.amp.^2) % figure(3); % plot(inputplot.frq(2:2:end),inputplot.amp(2:2:end)); % %Root mean square power calculations % pwr=0; % for k=1:512 % pwr=pwr+inputplot.amp(k)^2; % end % rms= figure(2); % power_timedomain = sum(abs(modu).^2)/length(modu); % This equation is intended to compute the rms of a given signal % poervector=sqrt(power_timedomain)*ones(1,length(modu)); % Crest_Factor=max(modu)/sqrt(power_timedomain); % This equation is used to compute the crest factor % CFvector=Crest_Factor*ones(1,length(modu)); % Create a vector to hold multiple values of the crest factor % plot(CFvector); % hold on % plot(poervector); % hold off % save('C:\Users\Laura\Documents\MATLAB\noisy_signal_GHz.txt', 'x', '-ascii'); l=1*150e-9; c=1*6.7e-9; r=10e3; num=1; den=[l*c l/r 1]; [numd,dend] = bilinear(num,den,samp_freq) y=filter(numd,dend,x); freq_y=fftshift(fft(y)/sample_size); plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(freq_y(1:sample_size))); % These statments are used to compute the crest factor based on the % avergaepower of the signal power_timedomain = sum(abs(y).^2)/length(y); % This equation is intended to compute the rms of a given signal poervector=sqrt(power_timedomain)*ones(1,length(y)); Crest_Factor=max(y)/sqrt(power_timedomain); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% toc % % save thetha.txt thetha -ascii % copyfile('TXA.txt',['TXA' num2str(z) '.txt']); % copyfile('thetha.txt',['Thetha' num2str(z) '.txt']); %end • The code used in CCstudio include "dsk6713_aic23.h" //support file for codec,DSK# #include "multitone.h" Uint32 fs = DSK6713_AIC23_FREQ_96KHZ; //set sampling rate short loop = 0; //table index short gain = 10; //gain factor interrupt void c_int11() //interrupt service routine { short sample_data; output_sample(multitone[loop]); //output data if(++loop>128) loop=0; //reset the loop when all samples are sent to the output return; } void main() { comm_intr(); //init DSK, codec, McBSP while(1); //infinite loop } //end of main Matlab code after editing %function[waveform]=mtpr_input(bin_start,bin_stop,sample_size,samp_freq,max_PAR) clear all clc %for z=1:100, clear x tic fcarrier = 24e3; A = 5; % Frequency of the RF carrier 1 GHz % The perak amplitude of the test signal sample_size=2^7; % Number of samples taken for simulation samp_freq=4*fcarrier; N_Tones=32; % bin_start=33; % bin_stop=256; % max_PAR=16; % missing=[48 72 96 120 144 168 192 216 240]; % Generating tone frequencies freq=(fcarrier/N_Tones)*(1:256); % m=0; % for k=1:N_Tones, % freq(k)=m+fcarrier/N_Tones; % m=freq(k); % num_tones(k)=k; % end %********************************************************************** %********************************************************************** %generation phases thetha(1:N_Tones)=0.6+sqrt(pi)*randn(1,N_Tones); %thetha(1:N_Tones)=0; %load('thetha.txt') %generatin amplitudes amp=ones(1,N_Tones); GAUSS_NOISE=0.2+sqrt(0.01)*randn(1,sample_size); noise signal with 0.2 mean and 0.01 variance %This statemnt generates a gaussian t=0; Ts=1/samp_freq; x=zeros(1,sample_size); for i=1:sample_size, for j=1:N_Tones, % Sampling interval x(i)=x (i)+amp(j)*sin(2*pi*t*freq(j)+1*thetha(j)); % samples taken from the 256 tones end % x(i)=x(i)+GAUSS_NOISE(i); multitone signal carrier(i) = A*sin(2*pi*t*fcarrier); modu(i)=x(i)*carrier(i); carrier by the multi tones % This statement adds a gaussian noise to the % The equation for the signal under test % modu is the signal obtained from multiplying the time(i)=t; t=t+Ts; end freq_x=fftshift(fft(x)/sample_size); freq_carrier=fftshift(fft(carrier)/sample_size); freq_modu=fftshift(fft(modu)/sample_size); figure(1); subplot(3,2,1) plot(linspace(0,Ts*sample_size,sample_size),x); title('Multitone signals with noise'); xlabel('time ns'); ylabel('Amplitude V'); subplot(3,2,2) plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(freq_x(1:sample_size))); title('Spectrum Multitone signals with noise'); xlabel('Freq GHz'); ylabel('Magnitude V'); subplot(3,2,3) plot(linspace(0,Ts*sample_size,sample_size),carrier); title('RF carrier'); xlabel('time ns'); ylabel('Amplitude V'); subplot(3,2,4); plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(freq_carrier(1:sample_size))); title('Spectrum carrier'); xlabel('Freq GHz'); ylabel('Magnitude V'); subplot(3,2,5) plot(linspace(0,Ts*sample_size,sample_size),modu); title('Carrier x dithered multitone'); xlabel('time ns'); ylabel('Amplitude V'); subplot(3,2,6); plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(modu(1:sample_size))); title('Spectrum carrier x dithered multitone'); xlabel('Freq GHz'); ylabel('Magnitude V'); modu=modu'; % plot(x); % % inputplot=Four(x,4e9); % %converting to db % inputplot.amp % figure(2); % plot(inputplot.frq(1:8:end),inputplot.amp(1:8:end)) % inputplot.amp=10*log10(inputplot.amp.^2) % figure(3); % plot(inputplot.frq(2:2:end),inputplot.amp(2:2:end)); % %Root mean square power calculations % pwr=0; % for k=1:512 % pwr=pwr+inputplot.amp(k)^2; % end % rms= figure(2); % power_timedomain = sum(abs(modu).^2)/length(modu); compute the rms of a given signal % % This equation is intended to poervector=sqrt(power_timedomain)*ones(1,length(modu)); % Crest_Factor=max(modu)/sqrt(power_timedomain); the crest factor % CFvector=Crest_Factor*ones(1,length(modu)); values of the crest factor % This equation is used to compute % Create a vector to hold multiple % plot(CFvector); % hold on % plot(poervector); % hold off % save('C:\Users\Laura\Documents\MATLAB\noisy_signal_GHz.txt', 'x', '-ascii'); l=2*150e-9; c=1*6.7e-9; r=10e3; num=1; den=[l*c l/r 1]; [numd,dend] = bilinear(num,den,samp_freq) y=filter(numd,dend,x); freq_y=fftshift(fft(y)/sample_size); plot(1/fcarrier*samp_freq*linspace(-5,5,sample_size),abs(freq_y(1:sample_size))); xlabel('frequency, MHz'); ylabel('Magnitude, V'); % These statments are used to compute the crest factor based on the % avergaepower of the signal power_timedomain = sum(abs(y).^2)/length(y); rms of a given signal % This equation is intended to compute the poervector=sqrt(power_timedomain)*ones(1,length(y)); Crest_Factor=max(y)/sqrt(power_timedomain); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(3) plot(x) xlabel('time, us') ylabel('amplitude, V') % power_timedomain = sum(abs(x).^2)/length(x); % Crest_Factor=max(x)/sqrt(power_timedomain); % Crest_Factor=max(x)/sqrt(power_timedomain); toc % % save thetha.txt thetha -ascii % copyfile('TXA.txt',['TXA' num2str(z) '.txt']); % copyfile('thetha.txt',['Thetha' num2str(z) '.txt']); %end i=0:length(x)-1; desired= round(25*x); %sin(1500)addnoise= round(100*sin(2*pi*(i)*312/8000)); %sin(312) fid=fopen('multitone.h','w'); %desired sin(1500) fprintf(fid,'short multitone[]={'); fprintf(fid,'%d,\n ' ,desired(1:length(desired)-1)); fprintf(fid,'%d' ,desired(length(desired))); fprintf(fid,'};\n'); fclose(fid); The sample vector of multitone short multitone[]={212, 208, 102, 21, -10, -13, -14, -9, 28, 45, 0, -98, -96, 10, 111, 85, -2, -8, 88, 175, 160, 85, 30, 13, -6, -42, -46, 4, 45, -15, -147, -208, -82, 75, 99, 3, -46, -3, 68, 110, 132, 108, 19, -81, -92, -30, -16, -61, -72, -37, -4, 16, 73, 118, 62, -61, -129, -129, -149, -176, -99, 35, 61, -66, -171, -152, -97, -114, -184, -182, -81, 75, 175, 162, 25, -66, 17, 161, 159, 25, -30, 69, 163, 139, 33, -65, -110, -66, 61, 149, 81, -24, -22, 47, 4, -96, -57, 93, 112, -29, -74, 32, 77, -29, -53, 120, 247, 117, -85, -121, -77, -112, -125, 4, 117, 7, -153, -76, 175, 257, 93, -44, 5, 66, -35, -168, -132, 59}; •