Agilent 33120A User's Guide
Contents
1. Tutorial Tutorial The Agilent 33120A is capable of producing a variety of signal waveshapes In order to achieve the greatest performance from the function generator it may be helpful if you learn more about the internal operations of the instrument This chapter describes basic signal generation concepts and gives specific details on the internal operations of the function generator e Direct Digital Synthesis starting on page 273 e Signal Imperfections starting on page 276 e Creating Arbitrary Waveforms starting on page 278 e Output Amplitude Control starting on page 280 e Floating Signal Generators on page 282 e Attributes of AC Signals starting on page 283 e Modulation starting on page 287 You can use an arbitrary waveform generator in a variety of applications where it might be otherwise difficult or impossible to generate complex output waveforms With an arbitrary waveform generator signal imperfections such as rise time ringing glitches noise and random timing variations can be easily simulated in a controlled manner Physics chemistry biomedicine electronics mechanics and other fields can benefit from the versatility of an arbitrary waveform generator Wherever things vibrate pump pulse bubble burst or change with time in any way there are possible applications limited only by your ability to provide waveform data The Agilent IntuiLink Arb Waveform Generation Software for Microsoft Wi2. Compute the modulation pre scaler divider S 5 truncated to integer value gt 1 Compute the number of points for the modulation waveform length 2xC P 8 x F rounded down to even number Waveshapes are automatically expanded or compressed to match length P computed above and downloaded into modulation RAM Example Assume that you need to phase continuously frequency hop between the following nine frequencies every 200 us 15 0 MHz 1 001 MHz 9 780 MHz 12 375 MHz 0 5695 MHz 3 579 MHz 0 8802 MHz 0 6441 MHz and 10 230 MHz Solution Create a modulation arbitrary waveform that is precisely sampled in FM modulation F 1 9x 200 us 555 555 Hz modulation frequency Round down in sixth digit to get modulation frequency to set S 624 555 555 1 1232 truncate to 1 2xC P S x F rounded down to even number 295 Chapter 7 Tutorial Modulation e Set the modulation frequency to 555 555 Hz e Set the carrier frequency to Max F Min F 2 7 784750 MHz e Set deviation pk frequency to Max F Min F 2 7 215250 MHz e Create and download a nine segment arbitrary waveform with the values shown below Each segment is 250 points long 2250 9 for a total of 2 250 points Use the DATA VOLATILE command download to achieve 12 bit frequency resolution for each point y is the new vertical value y mX b m 1 Deviation X is the original frequency point
3. 270 360 t lt One Cycle of Memory gt 279 48 Bit PIR Chapter 7 Tutorial Output Amplitude Control Output Amplitude Control The 33120A uses a 12 bit digital to analog converter DAC to convert the digital representation of a signal to an analog output voltage The DAC can create waveforms represented by 4 096 212 discrete amplitude levels All 4 096 amplitude codes are used for the built in waveforms Output levels from full maximum to minimum output are controlled by applying varying amounts of signal gain or attenuation to the signal created by the DAC as shown in the block diagram below The output waveform is always described by the full 12 bit vertical resolution You can download user defined arbitrary waveforms using less than the full 12 bit vertical resolution however it is recommended that you always use the full DAC amplitude resolution to minimize amplitude quantization errors as previously discussed eS Ge Clock See Anti Alias yeaa Filter N 500 48 Bit Wim SR ee ee oon aes PIR gt RAM gt DAC pa Sin eon VVV Oo lt 14 Bit 12 Bit s lt 5 Address Data Amplitude Data kr RA wy Step Attenuator Load 280 Chapter 7 Tutorial Output Amplitude Control As shown below the 33120A has a fixed output source resistance of 50 ohms During calibration output amplitudes are calibrated for both the open circuit voltage no load
4. b carrier frequency Deviation 1 078930044 Segment Value 1 0000 0 9402 0 2765 0 6362 1 0000 0 5829 0 9569 0 9897 0 3389 OANDOABRWNDN To Check Enable FM by sending the following commands FM STATE ON PM INT FREQ 555 555 DIAG PEEK 0 0 0 enter results lt Prescale S gt lt Points P gt 296 Specifications Chapter 8 Specifications Agilent 33120A Function Generator WAVEFORMS Standard Waveforms Sine Square Triangle Ramp Noise DC volts Sine x x Negative Ramp Exponential Rise Exponential Fall Cardiac Arbitrary Waveforms Waveform Length Amplitude Resolution Sample Rate Non Volatile Memory 8 to 16 000 points 12 bits including sign 40 MSa sec Four 16 000 point waveforms FREQUENCY CHARACTERISTICS Sine 100 Hz 15 MHz Square 100 Hz 15 MHz Triangle 100 Hz 100 kHz Ramp 100 Hz 100 kHz Noise Gaussian 10 MHz bandwidth Arbitrary Waveforms 8 to 8 192 points 8 193 to 12 287 points 12 288 to 16 000 points 100 wHz 5 MHz 100 Hz 2 5 MHz 100 Hz 200 kHz Resolution 10 wHz or 10 digits Accuracy 10 ppm in 90 days 20 ppm in 1 year 18 C 28 C Temperature Coefficient lt 2ppm C Aging lt 10ppm yr SINEWAVE SPECTRAL PURITY into 509 Harmonic Distortion DC to 20 kHz 70 dBc 20 kHz to 100 kHz 60 dBc 100 kHz to 1 MHz 45 dBc 1 MHz to 15
5. carrier output can be controlled using either triggered or externally gated methods When configured for triggered operation the function generator can output a carrier waveform with a user specified number of complete cycles Each time a trigger is received the specified number of complete cycles is output You can also specify a starting waveform phase in triggered operation Zero degrees is defined as the first data point in waveform memory The function generator will output the start phase as a dc output level while waiting for the next trigger Output dc offset voltages are not affected by burst modulation they are independently produced and summed into the function generator s output amplifier A three cycle bursted sine wave with 100 Hz burst rate In gated burst mode operation the rear panel Burst terminal is used to directly and asynchronously turn off the waveform DAC output The burst count burst rate and burst phase settings have no effect in this mode When the burst signal is true TTL high the function generator outputs the carrier waveform continuously When the burst signal is false TTL low the waveform DAC is forced to a zero output level Like triggered burst operation the output dc offset voltage is not affected by the external burst gate signal 291 Chapter 7 Tutorial Modulation For triggered burst operation the function generator creates an internal modulation s
6. modulation FSK the function generator s output frequency alternates between the carrier frequency and a second hop frequency The rate of frequency hops is controlled either by an internal source or from an external logic input FSK is essentially a special case of frequency modulation FM where the hop frequency is another way of specifying both the deviation and the modulating signal shape The modulating signal shape is always a square wave with an amplitude of zero to 1 The deviation is either positive or negative depending on whether the hop frequency is larger or smaller than the present carrier frequency as shown below The internal FSK rate generator specifies the period of the modulating square wave signal When selected the external FSK input replaces the internal FSK rate generator to directly control the frequency hop rate A TTL low input always selects the carrier frequency and a TTL high always selects the hop frequency The logic sense of the external FSK input can effectively be changed by interchanging the carrier and hop frequency values Deviation Hop Frequency Carrier Frequency See eee An FSK waveform with a 3 kHz carrier waveform and 500 Hz hop waveform the FSK rate is 100 Hz 290 Chapter 7 Tutorial Modulation Burst Modulation In burst modulation the function generator turns the carrier wave output on and off in a controlled manner The
7. 68 l q M3 5 X 0 6 4 PLACES All dimensions are shown in millimeters 301 302
8. In frequency modulation 100 modulation has a different meaning than in AM Modulation of 100 in FM indicates a variation of the carrier by the amount of the full permissible deviation Since the modulating signal only varies frequency the amplitude of the signal remains constant regardless of the modulation The function generator uses the deviation parameter to describe the peak frequency change above or below the carrier in response to a corresponding amplitude peak of the modulating signal For FM signals the bandwidth of the modulated signal can be approximated by BW gt 2 x Deviation Information Signal Bandwidth For wideband FM BW 2 x Information Signal Bandwidth For narrowband FM Narrowband FM occurs when the ratio of the deviation frequency to the information signal bandwidth is approximately 0 01 or less Wideband commercial FM radio stations in the United States use a 75 kHz peak deviation 150 kHz peak to peak and audio signals band limited to 15 kHz to achieve 200 kHz channel to channel spacing from the 180 kHz bandwidth 288 Chapter 7 Tutorial Modulation Frequency Sweep The 33120A performs phase continuous frequency sweeping stepping from the sweep start frequency to the sweep stop frequency with between 2 048 and 4 096 discrete frequency steps The direction of frequency sweeps can be varied by setting the stop frequency either above or below the start frequency Individual frequency steps are
9. MHz 35 dBc Total Harmonic Distortion DC to 20 kHz lt 0 04 Spurious non harmonic Output DC to 1 MHz lt 65 dBc Output gt 1 MHz lt 65 dBc 6 dB octave Phase Noise lt 55 dBc in a 30 kHz band SIGNAL CHARACTERISTICS Square wave Rise Fall Time lt 20 ns Overshoot lt 4 Asymmetry 1 5 ns Duty Cycle 20 to 80 to 5 MHz 40 to 60 to 15 MHz Triangle Ramp Arb Rise Fall Time 40ns typical Linearity lt 0 1 of peak output Settling Time lt 250 ns to 0 5 of final value Jitter lt 25ns OUTPUT CHARACTERISTICS Amplitude into 509 2 Accuracy at 1 kHz Flatness lt 100 kHz 100 kHz to 1 MHz 1 MHz to 15 MHz 1 MHz to 15 MHz 50 mVpp 10 Vpp 1 of specified output sine wave relative to 1 kHz 1 0 1 dB 1 5 0 15 dB 2 0 2 dB Ampl 3Vrms 3 5 0 3 dB Ampl lt 3Vims Offset into 509 3 Accuracy 5 Vpk ac dc 2 of setting 2 mV Output Impedance 50 ohms fixed Resolution 3 digits Amplitude and Offset Output Units Vpp Vrms dBm Isolation 42 Vpk maximum to earth Protection Short circuit protected 15 Vpk overdrive lt 1 minute 1 Add 1 10th of output amplitude and offset specification per C for operation outside of 18 C to 28 C range 1 year specification 2 100 mVpp 20 Vpp amplitude into open circuit load 3 Offset lt 2 X peak to peak amplitude 4 For square wave outputs add 2 of output
10. either linearly or logarithmically spaced based on the sweep mode setting Like FSK modulation described on the next page the sweep function is also a special case of frequency modulation FM All of the FM operations described on the previous page also apply to sweep when the following translations are applied Start Frequency Stop Frequency 2 Carrier Frequency Start Frequency Stop Frequency 2 Deviation The modulation waveshape for sweeps is a ramp wave or exponential wave for linear or log sweeps respectively The logic sense of the ramp or exponential modulation signal positive or negative ramp is selected when the stop frequency is either larger or smaller than the start frequency Like the FM function changes to sweep parameters cause the generator to automatically compute a modulation signal and download it into modulation RAM Similarly the sweep time parameter adjusts the period of the modulating waveform The sweep function also allows triggered operation This is like frequency modulating with a single cycle burst of the modulating signal beginning when a trigger is received Trigger signals can come from the rear panel Ext Trig terminal the front panel Single button or from commands over the remote interface A sine wave sweep from 50 Hz to 5 kHz with a linear 1 second sweep time 289 Chapter 7 Tutorial Modulation Frequency Shift Key Modulation In Frequency Shift Keying
11. following computation No expansion or compression is performed on the modulation waveform data for certain modulation frequencies 293 Chapter 7 Tutorial Modulation You can use the equations on the next page to determine specific waveform lengths and modulation frequencies when more precise control is needed Normally you should not have to perform these calculations The function generator incorporates an internal 8 bit 7 bits peak digital to analog converter DAC to create an analog copy of the modulation signal for amplitude modulation AM This signal is internally applied to a conventional four quadrant analog multiplier circuit to achieve amplitude modulation Similarly the generator uses digital signal processing to combine the carrier and modulation signals for frequency modulation FM The FM modulation signal maintains 12 bit resolution for frequency values The following equations and example describe the capabilities and limitations of the 33120A s internal modulation signal generator Parameter Definitions Maximum Point Clock C 5MSa s for AM 1 25 MSa s for FM Modulation Prescaler S integer numbers truncated from 1 2 3 22 Constant k 4 900 for AM 624 for FM Modulation Frequency F 10 mHz to 20 kHz for AM 10 mHz to 10 kHz for FM Points P values from 2 000 to 4 000 even numbers only rounded down 294 Chapter 7 Tutorial Modulation Equations
12. signal generator differs from a digital audio player because of its very precise control of the data stream input to the DAC In a DDS system the amplitude values for one complete cycle of the output waveshape are stored sequentially in random access memory RAM as shown in the figure below As RAM addresses are changed the DAC converts the waveshape data into a voltage waveform whose data values are loaded in RAM The frequency of the voltage waveform is proportional to the rate at which the RAM addresses are changed The 33120A represents amplitude values by 4 096 discrete voltage levels or 12 bit vertical resolution Waveforms may contain between 8 points and 16 000 points of 12 bit amplitude values The number of points in RAM representing one complete cycle of the waveshape or 360 is called its length or horizontal resolution Each RAM address corresponds to a phase increment equal to 360 points where points is the waveform length Therefore sequential RAM addresses contain the amplitude values for the individual points 0 to 360 of the waveform 0 90 180 270 360 t t t re 4096 Ok x 2047 DAC Codes y 7 N 0 t t t 0 3 999 7 999 11 999 15 999 Memory Address Points 274 Chapter 7 Tutorial Direct Digital Synthesis Direct digital synthesis DDS generators use a phase accumulation technique to control waveform RAM addressing Instead of using a counter to generate sequentia
13. the ac signal to deliver power to a resistive load heat The RMS value is equal to the dc value which produces the same amount of heat as the ac waveform when connected to the same resistive load For a dc voltage this heat is directly proportional to the amount of power dissipated in the resistance For an ac voltage the heat in a resistive load is proportional to the average of the instantaneous power dissipated in the resistance This has meaning only for periodic signals The RMS value of a periodic waveform can be obtained by taking the dc values at each point along one complete cycle squaring the values at each point finding the average value of the squared terms and taking the square root of the average value This method leads to the RMS value of the waveform regardless of the signal shape Peak to Peak and Peak Value The zero to peak value is the maximum positive voltage of a waveform Likewise the peak to peak value is the magnitude of the voltage from the maximum positive voltage to the most negative voltage peak The peak or peak to peak amplitude of a complex ac waveform does not necessarily correlate to the RMS heating value of the signal When the specific waveform is known you can apply a correction factor to convert peak or peak to peak values to the correct RMS value for the waveform Average Value The average value of an ac waveform is the average of the instantaneous values measured over one complete cycle For sine
14. waves the average amplitude is zero since the waveform has equal positive and negative half cycles Since the quantity of interest is the heating value of the signal the average value of a sine wave is taken to mean the average of the full wave rectified waveform The RMS value of a sine wave is equal to 1 11 times the sine wave average amplitude This relationship does not hold true for other waveshapes 285 Chapter 7 Tutorial Attributes of AC Signals dBm The decibel dB is commonly used to describe RMS voltage or power ratios between two signals By itself a decibel value has no particular meaning Decibels are a ratio or comparison unit and have no absolute meaning without knowledge of a reference or comparison unit When power comparisons are made to a 1 mW reference level the letter m is added to give dBm For power ratios such as dBm it is common to specify the resistance loading the voltage source Often the system resistance is added to the units by indicating dBm 5097 for a 509 resistance system dB 10 x log P Pref dBm 10 x logy P 0 001 where power P V R For a 509 resistance 1 mW of power corresponds to 0 224 VRMS dBm 502 Output Voltage Level 502 load 23 98 3 53 VRMS 13 01 1 00 VRMS 6 99 500 mVRMS 0 0 224 mVRMS 6 99 100 mVRMS 13 01 50 mVRMS Use the following conversions to determine dBm levels when connecting 75Q or 600 load resistances dBm 75 Q
15. 0A has both sides of the output BNC connector isolated from chassis earth ground As shown in the figure below any voltage difference between the two ground reference points Vground causes a current to flow through the function generator s output common lead This can cause errors such as noise and offset voltage usually power line frequency related which are added to the output voltage The best way to eliminate ground loops is to maintain the function generator s isolation from earth ground The function generator s isolation impedance will be reduced as the frequency of the Vground source increases due to low to earth capacitance Cle approximately 4000 pF for the 33120A If the function generator must be earth referenced be sure to connect it and the load to the same common ground point This will reduce or eliminate the voltage difference between devices Also make sure the function generator and load are connected to the same electrical outlet if possible RL 500 L fo oS Load L Van lt oH i Common He f z J Ce 2 Ri gt 10GO V Ea a ground pee a 7 fe N Af Xe R Lead Resistance 282 Chapter 7 Tutorial Attributes of AC Signals Attributes of AC Signals The most common ac signal is the sine wave In fact all periodic waveshapes are composed of sine waves of varying frequency amplitude and phase added together The individual sine waves are harmonically related to each oth
16. amplitude additional error 298 Chapter 8 Specifications Agilent 33120A Function Generator MODULATION CHARACTERISTICS AM Modulation Carrier 3 dB Freq Modulation Frequency Depth Source FM Modulation Modulation Frequency Peak Deviation Source Burst Modulation Carrier Frequency Count Start Phase Internal Rate Gate Source Trigger Source FSK Modulation Frequency Range Internal Rate 10 MHz typical Any internal waveform plus Arb 10 mHz to 20 kHz 0 05 to 2 5 kHz then decreases linearly to 0 4 at upper limit 0 to 120 Internal External Any internal waveform plus Arb 10 mHz to 10 kHz 0 05 to 600 Hz then decreases linearly to 0 8 at upper limit 10 mHz to 15 MHz Internal Only 5 MHz max 1 to 50 000 cycles or Infinite 360 to 360 10 mHz to 50 kHz 1 Internal or External Gate Single External or Internal Rate 10 mHz to 15 MHz 0 05 to 600 Hz then decreases linearly to 4 at upper limit 10 mHz to 50 kHz Source Internal External 1 MHz max FREQUENCY SWEEP Type Linear or Logarithmic Direction Up or Down Start F Stop F 10 mHz to 15 MHz Time 1ms to 500 sec 0 1 Source Single External or Internal REAR PANEL INPUTS External AM Modulation External Trigger FSK Burst Gate Latency Jitter 5 Vpk 100 Modulation 5 kQ Input Resistance TTL low true 1 3 us 25 ns SYSTEM CHARACTERISTICS Configuration T
17. and 400 Hz 10 Automatically sensed at power on CAT Il 50 VA peak 28 W average 0 C to 55 C 80 Relative Humidity to 40 C Indoor or sheltered location 40 C to 70 C Power off state automatically saved Three 3 User Configurable Stored States Arbitrary waveforms stored separately 254 4 mm x 103 6 mm x 374 mm 212 6 mm x 88 5 mm x 348 3 mm 4 kg 8 8 lbs 1 For 400 Hz operation at 120 Vac use the 100 Vac line voltage setting Safety Designed to EMC Vibration and Shock Acoustic Noise Warm Up Time Warranty Remote Interface Programming Language Accessories Included EN61010 CSA1010 UL 1244 EN61326 1 1997 1A 1998 MIL T 28800E Type Ill Class 5 data on file 30 dBa 1 hour 3 years standard IEEE 488 and RS 232 standard SCPI 1993 IEEE 488 2 User s Guide Service Guide Quick Reference Card IntuiLink Arb software RS 232 cable Test Report and power cord 300 Chapter 8 Specifications Agilent 33120A Function Generator PRODUCT DIMENSIONS 2 Soe pesi mra 103 6 mm g Cu oo00r00 g 254 4 mm Pe ss m 374 0 mm op000000g oooo0008 6 D 216 6 mm _ 2X 5 52 SQ m 348 3 mm M4 X 0 7 4 PLACES 19
18. and the terminated output voltage loaded The terminated output amplitude is calibrated for an exact 50 ohm load Since the function generator s output resistance and the load resistance form a voltage divider the measured output voltage of the function generator will vary with load resistance value and accuracy When the function generator s output is loaded with a 0 2 accuracy termination an additional negligible 0 2 amplitude error is created Using a 5 accuracy termination will add 5 additional error to specified output amplitudes 509 vgen A gt 509 Vioad If the function generator s output is measured with no load connected the output will be approximately twice the displayed amplitude Vgen instead of Vload In some applications you might continually use the function generator in a no load conditions In such applications remembering to double the function generator s displayed amplitude can cause many errors The 33120A allows you to specify the function generator s load condition using the OUTPUT LOAD command thus enabling the function generator to display the correct output amplitude 281 Chapter 7 Tutorial Floating Signal Generators Floating Signal Generators Many applications require a test signal which is isolated from earth ground for connection to powered circuits to avoid ground loops or to minimize other common mode noise A floating signal generator such as the 3312
19. cribed by a finite number of horizontal points length it has been sampled in time or quantized causing a phase truncation error Spurious signals caused by phase truncation introduce jitter into the output waveform This may be regarded as time and phase displacement of output zero crossings Phase truncation causes phase modulation of the output signal which results in spurious harmonics see the equation below For lower output frequencies the phase accumulator periodically does not advance RAM addresses causing the DAC to deliver the same voltage as recorded on the previous clock cycle Therefore the phase slips back by 360 points before continuing to move forward again When RAM address increments are the same on each cycle of the output phase truncation error and jitter are essentially zero All standard waveshapes in the 33120A are generated with at least 16 000 waveform points which results in spurious signals below the wide band noise floor of the DAC Phase Truncation Harmonics lt 20 x log P dBc where P is the number of waveform points in RAM 277 Chapter 7 Tutorial Creating Arbitrary Waveforms Creating Arbitrary Waveforms For most applications it is not necessary to create a waveform of any specific length since the function generator will automatically sample the available data to produce an output signal In fact it is generally best to create arbitrary waveforms which use all availab
20. dBm 50 Q 1 75 dBm 600 2 dBm 50 2 10 79 286 Chapter 7 Tutorial Modulation Modulation Modulation is the process of combining a high frequency carrier signal and a low frequency information signal How these signals are combined is determined by the specific type of modulation used The two most common types of modulation are amplitude modulation AM and frequency modulation FM The information signal that modulates or varies the carrier waveform can be of any form sine wave square wave arbitrary wave or random noise In general the carrier signal may also be of any shape but it is usually a sine wave of constant amplitude and frequency for most communications systems During modulation the simple carrier waveform is converted into a complex waveform by the lower frequency information signal Generally the higher frequency carrier waveform is used to efficiently transmit the complex modulated signal over long distances Amplitude Modulation AM Amplitude Modulation is a process of producing a waveform whose amplitude varies as a function of the instantaneous amplitude of the modulating information signal In other words the information signal creates an amplitude envelope around the carrier signal The 33120A implements double sideband transmitted carrier amplitude modulation similar to a typical AM radio station A constant is added to the AM modulating signal so that the sum is always grea
21. er that is to say the sine wave frequencies are integer multiples of the lowest or fundamental frequency of the waveform Unlike dc signals the amplitude of ac waveforms varies with time as shown in the following figure V pk V rms V avg V pk pk T t A sine wave can be uniquely described by any of the parameters indicated the peak to peak value peak value or RMS value and its period T or frequency 1 T 283 AC Attributes continued Chapter 7 Tutorial Attributes of AC Signals The magnitude of a sine wave can be described by the RMS value effective heating value the peak to peak value 2 x zero to peak or the average value Each value conveys information about the sine wave The table below shows several common waveforms with their respective peak and RMS values Waveform Shape Crest Factor C F AC RMS AC DC RMS o AES T 1 414 wa wy M a 1 732 Tp oz EU VE ea amp 0 a t C F C F C F t Each waveshape exhibits a zero to peak value of V volts Crest factor refers to the ratio of the peak to RMS value of the waveform 284 Chapter 7 Tutorial Attributes of AC Signals RMS The RMS value is the only measured amplitude characteristic of a waveform that does not depend on waveshape Therefore the RMS value is the most useful way to specify ac signal amplitudes The RMS value or equivalent heating value specifies the ability of
22. ernally the function generator incorporates a second lower speed and lower resolution DDS arbitrary waveform generator to produce the modulating signal independent of the carrier signal Internal modulation waveshapes range in length from 2 048 points to 4 096 points User defined arbitrary waveforms are automatically expanded or compressed in length as needed to fit within the required modulation waveform constraints Linear interpolation is performed on user defined arbitrary waveforms while the lengths of standard waveshapes are varied by decimation Due to the modulation sample rate and waveform size limitations the best case modulation signal frequency accuracy is approximately 0 05 of setting Unlike the main signal output discussed previously modulation waveshapes are sampled using a variable point clock to sample data loaded in modulation waveform RAM Internally the modulation point clock C and modulation waveform length are automatically adjusted to produce the modulation signal frequency desired For frequencies greater than C 2048 all modulation shapes are sampled up to the maximum modulating frequency A new modulation waveform is computed and loaded into modulation RAM each time the modulation type modulation waveshape or modulation frequency is changed Data in standard arbitrary waveform memory is not affected by modulation signal changes data is expanded or compressed and loaded directly into separate modulation RAM
23. ignal which is exactly synchronous with the carrier waveform This internal modulation signal is used to halt waveform memory addressing when the last data point is reached This modulation signal effectively gates the output on and off for the specified number of carrier wave cycles The modulation signal is then triggered by another internal burst rate signal generator which controls how often the specified carrier burst is output In external triggered burst operation the modulation signal trigger source is set to the function generator s rear panel Ext Trig terminal This source replaces the internal burst rate signal generator for pacing triggered bursts Changes to the burst count burst rate burst phase or carrier frequency will cause the function generator to automatically compute a new modulation signal and download it into modulation RAM It is not possible for the function generator to burst single cycles for all carrier frequencies because the internal modulation signal generator is not as capable as the main carrier signal generator The table below shows the function generator s carrier frequency and burst count limitations Carrier Minimum Frequency Burst Count 10 mHz to 1 MHz gt 1 MHz to 2 MHz gt 2 MHz to 3 MHz gt 3 MHz to 4 MHz gt 4 MHz to 5 MHz For sine square and arbitrary waveforms only akhwWNnN 292 Chapter 7 Tutorial Modulation Internal Modulation Source Int
24. imes 2 Function Change 80 ms Frequency Change 3 30 ms Amplitude Change 30 ms Offset Change 10 ms Select User Arb 100 ms Modulation Parameter Change lt 350 ms Arb Download Times over GPIB Arb Length Binary ASCII Integer ASCII Real 4 16 000 points 8 sec 81 sec 100 sec 8 192 points 4 sec 42 sec 51 sec 4 096 points 2 5 sec 21 sec 26 sec 2 048 points 1 5 sec 11 sec 13 sec Arb Download Times over RS 232 at 9600 Baud 5 Arb Length Binary ASCII Integer ASCII Real 6 16 000 points 35 sec 101 sec 134 sec 8 192 points 18sec 52 sec 69 sec 4 096 points 10 sec 27 sec 35 sec 2 048 points 6 sec 14 sec 18 sec 1 Trigger source ignored when External Gate is selected 2 Time to change parameter and output the new signal 3 Modulation or sweep off 4 Times for 5 digit and 12 digit numbers 5 For 4800 baud multiply the download times by two For 2400 baud multiply the download times by four etc 6 Time for 5 digit numbers For 12 digit numbers multiply the 5 digit numbers by two 299 Chapter 8 Specifications Agilent 33120A Function Generator GENERAL SPECIFICATIONS Power Supply 1 Power Line Frequency Power Installation Power Consumption Operating Environment Storage Environment State Storage Memory Dimensions W x H x D Bench Top Rack Mount Weight 100V 120V 220V 240V 10 switch selectable 50 Hz to 60 Hz 10
25. it om B Time Clock Cycles 275 Chapter 7 Tutorial Signal Imperfections The maximum output frequency with the condition that every waveshape point in RAM is output every waveform cycle is defined by Fout Felk Points The minimum number of points required to accurately reproduce a waveshape will determine the maximum useful output frequency using the same equation The rule governing waveforms is referred to as the Nyquist Sampling Theorem which states that you must include at least two points from the highest frequency component of the signal you are attempting to reproduce Signal Imperfections Most signal imperfections are easiest to observe in the frequency domain using a spectrum analyzer Sampling theory predicts the location and size of spurious signals resulting from the sampling processes used by DDS generators In fact since DDS generators use a fixed sampling rate 40 MHz for the 33120A spurious signals can be removed with a fixed frequency anti alias filter A 17 MHz ninth order elliptical filter providing a sharp cut off in excess of 60 dB attenuation for signals greater than 19 MHz is used for sine wave outputs A 10 MHz seventh order Bessel filter is used for non sine wave outputs The Bessel filter provides slower amplitude roll off for anti alias filtering but maintains linear phase response to minimize shape distortion for complex waveshapes The 33120A automatically selec
26. l RAM addresses an adder is used On each clock cycle the constant loaded into the phase increment register PIR is added to the present result in the phase accumulator see below The most significant bits of the phase accumulator output are used to address waveform RAM the upper 14 bits 214 16 384 RAM addresses for the 33120A By changing the PIR constant the number of clock cycles required to step through the entire waveform RAM changes thus changing the output frequency When a new PIR constant is loaded into the register the waveform output frequency changes phase continuously following the next clock cycle The 33120A uses a 48 bit phase accumulator which yields Felk 248 or approximately 142 nHz frequency resolution internally The phase accumulator output the upper 14 bits will step sequentially through each RAM address for smaller PIR values lower frequencies However when the PIR is loaded with a larger value the phase accumulator output will skip some RAM addresses automatically sampling the data stored in RAM Therefore as the output frequency is increased the number of output samples per waveshape cycle will decrease In fact different groups of points may be output on successive waveform cycles PIR k Phase ATX E Increment S ADDR aa Register z m MSB s l Time 48Bt 48 Bit 14 Bits Clock Cycles J Xe a a LS lt lt Phase PIR 2k Register al ADDR Ja p 48 B
27. le data 16 000 points long and the full range from 0 to 4 095 DAC codes For the 33120A you do not have to change the length of the waveform to change its output frequency All you have to do is create a waveform of any length and then adjust the function generator s output frequency Remember if you create an arbitrary waveform that includes three cycles of a waveshape for example the output frequency will be three times the value displayed on the function generator s front panel When creating arbitrary waveforms you have control of both the amplitude quantization and phase truncation errors For example phase truncation harmonics will be generated when a waveform is created using the full amplitude range of the DAC 12 bits but is created using only 1 000 waveform data points In this case the amplitude quantization errors will be near the noise floor while the time quantization error will produce harmonics near the 60 dBc level Similarly amplitude quantization harmonics will be generated when you create a waveform using less than the full amplitude resolution of the function generator For example if you use only one fifth of the available amplitude resolution amplitude quantization will produce harmonics below the 60 dBc level When importing data from instruments such as oscilloscopes the data will generally range between 1 024 and 4 096 time points and between 64 and 256 amplitude points When creating arbi
28. ndows is designed to make it easy to create and output arbitrary waveforms for the 33120A 272 Chapter 7 Tutorial Direct Digital Synthesis Direct Digital Synthesis Digital signal processing methods are used in many everyday applications Whether it is a digital audio compact disc player an electronic synthesized piano or a voice synthesized telephone message system it is obvious that complex waveforms can be easily created or reproduced using digital signal generation methods The 33120A uses a signal generation technique called direct digital synthesis or DDS The basic principle behind DDS is not unlike an audio compact disc As shown below for digital audio a stream of digital data representing the sampled analog signal shape is sequentially addressed from a disc This data is applied to the digital port of a digital to analog converter DAC which is clocked at a constant rate The digital data is then converted into a series of voltage steps approximating the original analog signal shape After filtering the voltage steps the original analog waveshape will be recovered The incoming data can be of any arbitrary shape as long as it matches the requirements of the particular DAC 16 bits for digital audio players l Anti Alias Filter Data E i PN D to A SS A io gt Converter 273 Direct Digital Synthesis continued Chapter 7 Tutorial Direct Digital Synthesis A direct digital synthesis DDS
29. ter than zero for lt 100 modulation as this equation shows D is the modulation depth 0 lt D lt 1 2 Am is the modulating signal with peak amplitude lt 1 Fc is the carrier frequency 1 Dx Am x sin 27x x Fex t 2 An AM waveform with 80 modulation depth The carrier waveform is a 5 kHz sine wave and the modulating waveform is a 200 Hz sine wave 287 Chapter 7 Tutorial Modulation In amplitude modulation the amplitude of the carrier varies between zero and twice its normal value for 100 modulation The percent modulation depth is the ratio of the peak information signal amplitude to the constant When amplitude modulation is selected the 33120A automatically reduces its peak to peak amplitude by one half so that a 100 modulation depth signal can be output Amplitude settings are defined to set the 100 peak to peak amplitude independent of the modulation depth setting Vrms and dBm amplitude settings are not accurate in AM since signals are very complex Frequency Modulation FM Frequency Modulation is a process of producing a wave whose frequency varies as a function of the instantaneous amplitude of the modulating information signal The extent of carrier frequency change is called deviation The frequency deviations are caused by the amplitude changes of the modulating information signal You can set the amount of the peak frequency in FM with the deviation parameter
30. trary waveforms the function generator will always attempt to replicate the finite length time record to produce a periodic version of the data in waveform memory As shown on the next page it is possible that the shape and phase of a signal may be such that a transient is introduced at the end point When the waveshape is repeated for all time this end point transient will introduce leakage error in the frequency domain because many spectral terms are required to describe the discontinuity 278 Chapter 7 Tutorial Creating Arbitrary Waveforms Leakage error is caused when the waveform record does not include an integer number of cycles of the fundamental frequency Power from the fundamental frequency and its harmonics is transferred to spectral components of the rectangular sampling function Instead of the expected narrow spectral lines leakage can cause significant spreading around the desired spectral peaks You can reduce leakage errors by adjusting the window length to include an integer number of cycles or by including more cycles within the window to reduce the residual end point transient size Some signals are composed of discrete non harmonically related frequencies Since these signals are non repetitive all frequency components cannot be harmonically related to the window length You should be careful in these situations to minimize end point discontinuities and spectral leakage 0 90 180 270 360 0 90 180
31. ts the appropriate filter when the output function is selected All digital to analog converters including those used in DDS generators produce spurious signals resulting from non ideal performance These spurious signals are harmonically related to the desired output signal At lower frequencies the 33120A s 12 bit waveform DAC produces spurious signals near the 74 dBc level decibels below the carrier or output signal as described by the equation on the following page The 33120A uses the complete vertical resolution N 1 of the DAC for all internal waveshapes thus minimizing amplitude quantization error 276 Chapter 7 Tutorial Signal Imperfections At higher output frequencies additional DAC errors produce non harmonic spurious outputs These are signals folded back or aliased to a frequency within the signal bandwidth A perfect DAC will also produce a wideband noise floor due to amplitude quantization The noise floor for a 12 bit DAC will be near the 74 dBc level this corresponds to a noise density of 148 dBc Hz for sine wave outputs from the 33120A Amplitude Quantization lt 20 x log Nx 4096 1 8 dBc where N is the fraction of available DAC codes used to describe the signal waveshape 0 lt N lt 1 Another type of waveform error visible in the frequency domain is phase truncation error This error results from time quantization of the output waveform Whenever a waveshape is des
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