SAMPLING NOTES
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`RPX-Farmwald Ex. 1037, p 1
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`SAMPLING NOTES
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`Copyright © 1964 by Tektronix,
`Inc., Beaverton, Oregon. Printed in
`the United States of America. All
`rights reserved. Contents of this
`publication may not be reproduced
`in any form without permission of
`the copyright owner.
`
`Scanned January 13, 2009.
`Revision 1.0
`
`Tektronix, Inc.
`S . W . M i l l i k a n W a y • P . O . B o x 5 0 0 0 B e a v e r t o n , O r e g o n • P h o n e M I 4- 0 1 6 1 • C a b l e s : T e k t r o n i x
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`Objective
`
`These sampling notes are offered as an aid to the user
`of Tektronix sampling systems. Concepts and systems are
`discussed, with references of some texts included for addi-
`tional study.
`
`Why Sampling Oscilloscopes
`The general need for sampling systems is caused by the
`normal gain-bandwidth limitations of amplifie rs. The state
`of the electronic art has not advanced to the point where
`fractional -nanosecond low-level signals can be displayed
`directly. A sampling system looks at a small portion of a
`waveform, remembers the amplitude for as long as desired,
`and presents a display of the instantaneous amplitude, all
`without amplifying the signal directly. It looks at the wave-
`form again slightly later in time, presents a new portion
`of the display, and ultimately shows a complete display
`in reconstructed form.
`
`Fig. 1 illustrates the reconstruction of a repetitive square
`wave, showing that the crt display is a series of dots rather
`than the normal oscilloscope continuous presentation. In
`the illustration, a series of sampling pulses is superimposed
`on the input waveforms. The pulse samples, and not the
`actual input signal, are displayed by the oscilloscope. At
`the peak of each sampling pulse the crt of the oscilloscope
`is unblanked and a spot appears. A large number of such
`spots forms the display. The number of dots in a display
`is variable over a range of 50 to 500 or more, depending
`upon the particular instrument.
`
`The sampling oscilloscope operates from repetitive signals,
`although not necessarily signals with a constant repetition
`rate. A small portion of each cycle of the signal is measured
`and a dot is displayed which indicates the amplitude of the
`sampled portion of the signal. The dot is horizontally
`positioned proportional to the point in time-space sampled.
`
`Sampling systems (and conventional oscilloscopes) have
`a maximum operating repetition rate. Signals below this rate
`may have considerable repetition rate jitter and still be
`presented without appreciable display jitter. Signals above
`the maximum repetition rate will be "counted down". Only
`those repetitions occurring after the sampling system recovery
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`SAMPLING NOTES
`
`will be displayed. Since the signals are repetitive in char-
`acter, the missed cycles are of no significance (as in con-
`ventional oscilloscopes).
`
`Pulse Definitions And Coaxial Cable
`Characteristics
`Gaussian pulses amplified by a gaussian system take the
`general nature of Fig. 2. The performance of the system is
`known by measuring the 10% to 90% risetime of the output
`pulse when the input pulse 10% to 90% risetime is several
`times faster.
`
`Fig. 2. Response of a gaussian amplifier to a gaussian pulse.
`
`Pulses handled by transmission lines (such as for 50-ohm
`input sampling) are not treated in a gaussian manner. Fig.
`3(a) represents the step- function response of transmission
`lines commonly used for pulse work having a decibel attenua-
`tion that varies as the square root of frequency.' The time,
`T0 (Tee Naught), is defined as the interval measured from
`the start of the output pulse to the point at which E out= 0.5
`Ein. Fig. 3(a) relates to coaxial lines with negligible dielectric
`loss. Good coaxial cables 10% to 90% risetime is usually
`about 30 times T0. An interesting character of transmission
`lines is that an increase in length of 2 times increases T0 4
`times (see Fig. 3(b)). Fig. 3 does not include effects that de-
`pend on the way in which the cable is used. Examples of such
`
`Fig. 1. Displaying input waveforms by means of the sampling technique.
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`Sampling Notes
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`Fig. 3a. Step-function response of transmission lines for which decibel attenuation varies as the square root of frequency. The time
`
`T0, is defined as the interval measured from the start of the output pulse to the point at which Eo u t = 0.5 E i n.
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`
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`Fig. 3b. Calculated variation of T0 with cable length for typical coaxial cables. Example— 100 ft. RG8, T0 ˜ 3.6 X 10 - 10: 200 ft. RG8,
`T0 ˜ 1.4 X 10 - 9.
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`Sampling Notes
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`quantities are the risetime of the input pulse and imperfect
`terminations. The curve does not take into account the inevit-
`able small variations of characteristic impedance along the
`line. The impedance variations will generally degrade the
`risetime of the output pulse by reflecting portions of the faster
`rising parts of a pulse being transmitted.
`
`an open- cycle sampled- data system2. See Fig. 4. The crt
`b e a m i s h e l d o f f t h e p h o s p h o r e x c e p t w h e n a s a m p l e i s
`taken. There is no prediction of what the next sample
`t h e
`is
`t h e r e a n y m e m o r y o f
`volta g e w i l l b e , n o r
`p r e v i o u s l y sampled voltage. The memory circuit resets to
`zero at the end of a relatively short display time.
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`Tektronix Sampling Systems
`
`Two general systems of sampling are in use in Tektronix
`instruments. The first form, the Type N Unit, is known as
`
`Fig. 4. Simplified block diagram of Type N Unit, an open-cycle
`sampled-data system.
`
`The second form, the Type 3S76, Types 4S1, 4S2, 4S3 and
`3S3, are known as an error- sampled feedback system.
`The sampling circuitry employs a zero- order hold memory
`last sample. A
`that remembers
`the amplitude of
`the
`transition is made only when there is a change in the signal
`or a drift in the system. This second sampling system looks at
`the incoming signal, remembers it, and then only has to
`the next sample. The
`make a display correction
`for
`system can also be described as a slide- b a c k f e e d- back
`s a m p l i n g s y s t e m w i t h ratchet memory (see Fig. 5). The
`ratchet memory is not reset, but the display is blanked
`during the time of transition from one sample to the next.
`
`The input circuit of the first system (the Type N Unit)
`is shown in the simplified diagram of Fig. 6. Diode D1 is
`normally reverse biased by the VERT. POSITION control.
`The signal modulates the reverse bias so that the interrogate
`p u l s e h e i g h t , a s f e d t o t h e s t r e t c h a m p l i f i e r , v a r i e s w i t h
`the signal. The stretch amplifier has a time constant long
`signal- modulated
`enough
`to
`effectively
`stretch
`the
`sampling- p u l s e t o a b o u t 2 5 0 n s e c . T h e v e r t i c a l s y s t e m
`ultimately presents a 1-µsec pulse to the oscilloscope for
`each sample taken; then the system is reset to zero,
`ready for the next sample.
`
`Fig. 5. Tektronix slide -back feed-back sampling system.
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`Sampling Notes
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`
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`Fig. 6. Simplified Type N input circuit.
`
`feed-back
`the slide -back
`input circuit of
`The
`sampling system is presented in simplified form in
`Fig. 7. The sampling bridge type gate is held reverse
`biased except during the short interrogate pulse
`duration. Reverse biasing the gate prevents the
`signal from being passed to the first amplifier. If the
`sampling gate is a balanced system, the interrogate
`pulse forward biases the gate and permits the signal
`to pass, without the amplifier or input system seeing
`the pulse. The balanced bridge sampling system
`operates with less noise and better linearity than the
`single diode open-loop system.
`When the sampling gate passes the signal, C1
`starts to charge. C1 charges to a fraction (such as
`25% in the Type 4S1) of the difference between the
`signal and feedback voltages at the time of a sample.
`Fig. 8 is an equivalent circuit of the sampling input at
`the time the gate is forward biased. C1 is stray and
`input capacity at the grid of the input amplifier. The
`equivalent circuit shows a group of impedances in
`
`Fig. 7. Basic 50 -ohm input of some Tektronix '3' and '4' Series sampling units.
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`Sampling Notes
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`Fig. 8. 50 -ohm '3' and '4' Series sampling input equivalent circuit.
`
`series. The impulse speed of the equivalent circuit is
`slower than the interrogate time, thus the input signal cannot
`be fully impressed upon the amplifier grid. Since only 25% of
`the difference signal appears at the input grid, the system is
`said to have a 25% sampling efficiency. The amplifier and
`memory circuits of Fig. 7 make up the difference in signal
`amplitude and feed back the correct voltage so the input
`bridge and C1 rest at the value of the signal during
`interrogation. By applying feedback to the bridge, the error
`signal is kept to a reasonable minimum, thus keeping the
`interrogate pulse kickback into the input cable very small.
`Fig. 5 illustrates how the sampling input amplitude is brought
`up to the true value of the input signal by the amplifier and
`memory circuits.
`The memory gate connects the memory circuit only long
`enough to respond to the amplified 25% sample signal, then
`disconnects
`it. This prevents
`the memory
`from also
`responding to its own feedback signal.
`Fig. 9 shows the signal and feedback voltages for six
`samples along the rise of a step waveform.
`Sample number 1. The voltage at C1 and the input are
`equal, so the system voltage remains at zero.
`Sample number 2. The sampled voltage equals 0.25 volt.
`Cl charges to 25% of the difference between the sampled
`voltage and the voltage at C1 or 0.0625 volt, then the
`feedback brings the voltage up to the sampled voltage true
`value of 0.25 volt.
`Sample number 3. The voltage difference between the
`sampled voltage of 0.5 volt and C1 is again 0.25 volt. Again
`the charge of C1 changes 25% of the difference, and the
`feedback raises the voltage of C1 to 0.5 volt.
`This process continues until sample number 6. There is no
`change in input voltage between sample number 5 and
`sample number 6, therefore, there is no difference between
`the charge of C1 and the sampled voltage. The sys tem
`remains at a constant voltage.
`
`Risetime Controlled By Interrogate Pulse
`Duration
`The length of time a sampling bridge is forward biased and
`connects the signal to C1 directly controls the minimum pulse
`risetime a sampling system can display. The duration of the
`bridge forward bias is controlled by the length of
`
`Fig. 9. Voltage changes at C1 of Fi g. 8 as samples are taken.
`The above is true only when the loop gain is 1.
`
`time the interrogate pulse breaks through the reverse bias.
`Thus sampling systems use special circuitry to make the
`interrogate pulse duration as short as is consistent with noise
`and diode recovery time. The interrogate pulse in some
`Tektronix slide-back fe ed-back sampling systems is produced
`by a snap-off diode and a short clip-line. The effective pulse
`duration is then adjusted by controlling the peak value of the
`pulse that is allowed to forward bias the sampling gate. Fig. 7
`shows graphically how the interrogate pulse breaks through
`the sampling gate reverse bias. The reverse bias volta ge is
`shown by dashed lines through the interrogate pulses. The
`sampling time is altered by changing the reverse bias on the
`sampling diodes2.
`
`Loop Gain
`Loop gain refers to the product of the sampling efficiency
`and the amplifier and memory gains. The loop gain equals 1
`when the voltage of C1 (Fig. 7), after memory feedback, is
`equal to the sampled voltage.
`The loop gain of a closed-loop sampling system can be
`altered by changing the input amplifier gain, the duration of
`the interrogate pulse, or the input impedance into the
`sampling gate. Changing the latter two alters the sampling
`efficiency and thus the loop gain.
`
`Sampling Density
`The number of samples taken per unit equivalent time is
`called the sampling density. For example: when the sweep
`rate is 10 nsec/div and when taking 100 samples per division,
`the equivalent time interval between dots is 0.1 nsec. This
`permits the system to measure time by counting the number
`of dots, such as is done by a digital unit.
`
`Dot Transient Response (Apparent Risetime
`Sampling Density Dependence)
`When the loop gain is adjusted to be other than 1, the
`appearance and measured risetime of an input signal will vary
`with changes in sampling density. This is usually true for low
`sampling densities. When the display is altered by changing
`the samples per division, it is referred to as dot transient
`response error. A good test for such false displays is to
`change the sampling density by changing the number of
`samples per division on the crt by a factor of two or m ore. If
`the equivalent wave shape does not change signifi cantly, the
`dot transient response is good enough.
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`Sampling Notes
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`Fig. 10. Dot transient response changes with changes in loop gain.
`Fig. 10 shows three conditions of loop gain vs two con-
`ditions of sampling density. In the illustration, solid traces
`show over 1000 samples per equivalent unit of time, and
`the dot traces show about 10 samples per equivalent unit of
`time. Note that with high sampling density the dot transient
`response errors are indiscernible. Fig. 10(a) shows a loop
`gain of 1. Changing sampling density does not significantly
`change apparent risetime. Fig. 10(b) shows a loop gain
`greater than 1. High sampling density shows the same
`risetime as (a), while low sampling density shows alternate
`overshoot and undershoot. Fig. 10(c) shows a loop gain
`less than 1. High sampling density shows correct risetime,
`
`while a low sampling density shows an increased (longer)
`risetime. The significance of this is the loop gain can be in
`error by a large factor, and yet the display will be calibrated,
`provided there is high dot density and correctly triggered
`sampling.
`
`Smoothing Of Random Noise
`The dot transient response discussion shows that with a
`high sampling density the loop gain can be less than 1
`without degrading the display significantly. If you reduce the
`loop gain 50%, the display dots will move only one half the
`normal amount. Noise spikes will be reduced one half.
`Thus, while using a sampling system at high sensitivities , if
`random noise is apparent, reducing the loop gain can im -
`prove the display. Note that this is true only for random
`noise, and not for systematic noise, since systematic
`(repetitive) noise is looked at as being part of the signal.
`
`Tektronix slide-back feedback sampling units have a loop
`gain control called SMOOTHING. Full smoothing reduces
`random noise typically 3 or 4 times. Always check that there
`is sufficient dot density to warrant the degree of smoothing
`used by changing the dot/division control.
`
`Changing Sensitivity
`Fig. 11 illustrates a method used to change the overall
`input to memory output gain while maintaining a sensibly
`constant dot transient response. If the system is at maxi -
`mum sensitivity, the ac amplifier is set for maximum gain
`and there is maximum attenuation of the feedback. This
`allows the memory output to be at a standard level (so
`many millivolts per division) for a given small input, while
`sending just the right amount of feedback to the input stage.
`To reduce system sensitivity, some attenuation is inserted
`in the ac amplifier. Now the memory output will be at the
`standard level with a larger input, and therefore the feed-
`back must be a larger feedback to the input amplifier. Thus
`the system loop gain remains constant with changes i n sen-
`sitivity.
`
`Adding a Dc Offset Voltage To The Signal
`Since the sampling bridge can operate linearly with
`signals from ±1 to ±2 volts depending upon the unit in use,
`it is possible to view portions of a fairly large signal at high
`sensitivity. To bring the desired portion of the large off -
`screen signal into view, a dc offset voltage is added to the
`feedback circuit. Fig. 12 shows the general form of a signal
`offset voltage circuit, designed to permit changing the
`feedback attenuation without shifting the display up or
`down. With this system, any portion of a pulse can be
`viewed with sensitivities up to about 2 mv/cm.
`
`Getting The Signal To The Input
`Sampling system input circuits range from 50-ohm
`its own
`coaxial
`to high-impedance probes. Each has
`advantages, and none is best for all applications.
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`Sampling Notes
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`Fig. 11. Addition of an attenuator system.
`
`Fig. 12. Addition of a signal dc offset voltage.
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`Sampling Notes
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`Probes For Sampling Systems
`Attenuator probes currently available for 50-ohm sam-
`pling systems include both passive and ca thode follower
`types having input characteristics ranging from 500 ohms
`and 0.8 pf capacitance, 'to 10 megohms at dc and 1.3 to
`3.6 pf capacitance. Each probe is analyzed for both
`resistive and capacitive input, with data shown in Fig. 13. 3
`A com bination of the Type 4S2 Dual Trace Sampling Unit
`and the miniature P6034 Probe (not in Fig. 13) has an
`upper frequency 3db point of 3500 mc and a risetime of 100
`picoseconds or less from a 25-ohm source.
`Miniature probes for direct sampling systems have less
`obvious limitations than passive and cathode follower
`probes.3 Signal generator impedance affects the direct
`sampling probe by altering the system loop gain. This how-
`ever, need not be a great problem since nanosecond
`circuits
`rarely exist
`in high-impedance
`form. Source
`impedance sensitivity can usually be no problem
`in
`Tektronix slide-back feedback sampling systems that have
`the ability to operate with a high sampling density.
`The Tektronix P6038 Direct Sampling Probe can be used
`to signal trace directly within a test circuit or can be
`inserted into special chassis or coaxial fittings.
`The P6038 Probe can be compared with any standard
`oscilloscope probe. The bandwidth (risetime) is limited by
`internal circuitry, and by
`the source resistance--input
`capacitance time constant. The P6038 input resistance is
`100 K at low frequencies, with a quite low (nominally 2 pf)
`input capacitance, allowing very fast response to low-
`impedance signals.
`The major difference between the P6038 and standard
`attenuator probe is the sampling circuit. A small signal is
`sent out of the probe tip to the signal source at each
`sample. This can be reduced by a factor of ten by using the
`10X Attenuator supplied. Normal sampling -pulse kickout
`(system at equilibrium) is less than 50 mv, and less than 5
`mv with the 10X Attenuator. The kickout is not seen by the
`sampling system, and if more than about 1/3-nsec delay
`cable is used between the signal source and the probe tip,
`the kickout is not seen by the source until after the next
`sample is taken.
`
`Sampling Timing Systems
`
`following discussion about sampling horizontal
`The
`(timing) systems outlines
`the systems
`typical of
`the
`Tektronix '3' and '5' series plug-in units.
`To recreate a waveform using sampling techniques,
`samples must be taken over the entire waveform. Taking a
`sample of the leading edge of the waveform is easy; a
`trigger circuit is used to trip an interrogate (strobe) pulse
`generator directly. A block diagram of this system is shown
`in Fig. 14.
`In practice, the system represented by Fig. 14 would not
`be able to sample on the very front of the waveform, be-
`cause of the finite time delay in the trigger and strobe
`generator circuits. Therefore, a time delay must be intro-
`duced between the vertical signal input and the sampling
`circuit. If the vertical signal input is 50 O, a 50 O coax cable
`may be used to obtain the necessary delay. A delay of
`approximately
`50
`nanoseconds
`(solid
`polyethelene
`dielectric representing about 33 feet of 50 O coax), is
`generally used. See Fig. 15.
`
`Fig. 13. Input resistance and impedance of Tektronix probes suit-
`
`able for use with sampling systems.
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`F ig . 14. Simple trigger system.
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`Fig. 15. Simple trigger system with signal delay so leading
`
`edge can be viewed.
`
`Although the system represented by Fig. 15 would
`be able to sample on the leading edge of an incoming
`waveform, it probably would not be able to sample in
`the middle of the waveform or at the trailing edge.
`Practical trigger circuits can generally "recognize" only
`the leading edge (or transition) of a waveform. In order
`to sample in the middle of the waveform, a time delay
`must be inserted between the trigger circuit and the
`strobe generator.
`
`Since long-time delays may be necessary (up to a
`millisecond), and since
`the delay should be
`continuously variable, an electronic delay is used. The
`strobe generator is now tripped by the delayed trigger
`output o f the variable delay circuit. If a sufficient range
`of delay is available, samples may now be taken over
`the entire waveform. See Fig. 16. Fig. 17 is the Type N
`Unit.
`
`Functionally, the variable delay circuit is identical to
`the delayed trigger pick-off in the Tektronix Type 535
`Oscilloscope. The
`trigger circuit
`recognizes
`the
`incoming waveform and initiates a voltage ramp or
`sweep. The voltage ramp is fed into a comparison
`circuit, or comparator, along with a dc voltage. When
`the ramp reaches the level of the dc voltage, the
`comparator puts out a trigger pulse called the delayed
`trigger. The time delay between the trigger input and
`the delayed trigger output may be changed by varying
`either the dc voltage or the slope of the ramp.
`
`Sampling Notes
`
`Usually the dc voltage is changed to obtain a vernier
`delay, and the slope of the ramp is changed to change the
`range of the vernier. A block diagram of the delayed
`trigger circuit is shown in Fig. 18.
`
`The delays needed in sampling systems are generally
`much shorter than those available from the delayed trigger
`of a Type 535;
`therefore,
`the circuitry
`is different.
`However, a voltage ramp, now called the "fast ramp'', is
`still compared to a variable dc voltage to obtain the
`variable time delay needed to sample a long the full length
`of a wave form. The sampling system block diagram now
`takes the form of Fig. 19.
`
`If the dc voltage in Fig. 19 is increased each time a
`sample is taken, comparison will take place progressively
`further along the fast ramp. Thus, there is a progressive
`increase in the time delay between trigger recognition and
`sampling. This causes each sample to be taken on a
`different part of the incoming signal.
`
`A complete sampling system, therefore, includes an
`incremental
`voltage-advancing circuit or
`"staircase
`generator". The staircase generator is made to advance
`one increment immediately after each sample is taken, by
`feeding the delayed trigger output of the comparator into
`the staircase generator. By advancing
`the staircase
`immediately after a sample
`is
`taken,
`the staircase
`generator is given the maxi mum time to reach its new dc
`level before the next fast ramp arrives. Substituting a
`staircase generator for the variable dc voltage, the block
`diagram changes to Fig. 20.
`
`time spacing
`The real
`is determined only by the
`repetition rate of the signal (up to the maximum sampling
`rate of the oscilloscope). The equivalent time spacing is
`determined only by the fast ramp slope and the amplitude
`of each stairstep. Therefore, the equivalent time of a
`sampling display is independent of the real time of the
`display and vice- versa.
`
`If the fast ramp is a linear voltage/time ramp and if the
`stairstep is advanced in uniform increments, the spacing
`of the Isamples along the incoming signal will be uniform
`in equivalent time.
`
`Fig . 16. Trigger system that can 'look' at leading or middle of a waveform.
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`Sampling Notes
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`Fig. 17. Simple block diagram of Tektronix Type N Unit with external trigger system.
`
`samples depends on the repetition rate of the signal. How-
`ever, by using 12 samples to reconstruct a picture of the
`waveform, we are in effect pretending that all of the
`samples were taken on one pulse. If this were true, the time
`between samples would be only 1 nanosecond (12 samples
`along the 12-nanosecond pulse). This is the equivalent
`time between samples. See Fig. 21.
`To reconstruct a signal, the samples must be spaced
`horizontally in the proper time sequence. This is done by
`feeding the stairstep into the horizontal amplifier so that the
`trace moves one increment horizontally as each sample is
`taken. The relationship between the increment of horizontal
`distance per sample and the equivalent time per sample will
`determine the (equivalent) sweep time/div. Adding this
`function, the block diagram becomes that of Fig. 22.
`To take a specific example, suppose that the amplitude of
`staircase going into the comparator is 50 m v/step, where
`one step equals one sample. If the fast ramp rises 50 mv
`nsec, the equivalent time per sample will be 1 nanosecond.
`
`Fig. 18. Block diagram of a delayed trigger circuit.
`
`To understand the meaning of "equivalent time", consider
`the following case: Recreate a repetitive pulse 12 nano-
`seconds wide by taking 12 samples, one sample per incom -
`ing signal. In this case, the real time between successive
`
`Fig. 19. Addition of a variable trigger circuit that allows triggering to progress along signal waveform.
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`Sampling Notes
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`Fig. 20. An automatic variable trigger circuit.
`
`Fig. 21. Real Time and Equivalent Time relationship.
`
`Fig . 22. Completed block diagram of the Tektronix slide -back feedback sampling systems.
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`Sampling Notes
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`The previous discussion referred to a staircase to sample
`at various points along a signal (common practice is to say
`that the strobe pulse "slews" along the signal). Under
`certain conditions the stairstep waveform will not resemble
`its namesake very closely. Actually, the staircase advances
`one step per sample, so that the voltage versus the number
`of samples taken looks like Fig. 24. If the incoming signal
`repeats at regular intervals, the spacing of the steps on the
`staircase will be uniform in real time, as shown in Fig. 24.
`
`Fig. 23. Fast ramp waveform that will produce an equivalent time
`per sample of 1 nanosecond.
`
`See Fig. 23. To adjust the gain of the horizontal amplifier
`so that each step advances the trace horizontally 1 milli-
`meter, 10 samples (at an equivalent time per sample of 1
`nanosecond) will be required per cm; the sweep time/cm,
`therefore, will be 10 nanoseconds. In other words, the
`(equivalent) time per sample, times the number of samples
`per division, equals the (equivalent) time per division:
`(Time/sample) (Samples/div) = Time/di v.
`Returning to the specific example, leave the fast ramp
`and the horizontal gain unchanged, but change the ampli-
`tude of each stairstep from 50 mv to 100 mv. This will
`result in a horizontal step of 2 mm/sample or 5 sample/cm.
`The equivalent
`time/sample will
`increase
`from 1
`nanosecond to 2 nanoseconds. The resulting time/cm may
`now be calculated:
`(2 nsec/sample) (5 samples/cm) = 10 nsec/cm.
`Changing the amplitude of the stairstep thus does not
`affect the time/cm calibration of the display, provided the
`horizontal gain and
`the
`fast
`ramp slope
`remain
`unchanged. The SAMPLES/DIV. control on sampling
`oscilloscopes merely changes the amplitude of each step
`in the staircase.
`
`Fig.25. Staircase voltage changes with irregular repetitive signal
`sampling .
`
`However, if the incoming signal recurs at an irregular rate,
`the spacing of the samples (and steps) will be nonlinear in
`real time as shown in Fig. 25.
`Therefore, do not expect the stairstep to always look like
`a uniform stairstep when observed in real time. Note that
`irregular spacing of the samples in real time will not cause
`irregular spacing in equivalent time, since the equivalent
`time calibration is independent of the repetition rate of the
`incoming signal. Problems will arise, however, when
`equivalent time phenomena are viewed on a real time
`(conventional) oscilloscope.
`
`References
`
`1. Transient Analysis Of Coaxial Cables, Considering
`Skin Effect, Wiginton and Nahman, Proc. IRE, Vol.
`[4?] pp 166- 174. February 1957.
`
`2. Sampled- Data Control Systems, Ragazzini and
`Franklin McGraw - Hill Book Co. 1958.
`
`3. In And Out Of Circuits With Probes, Winningstad,
`Tektronix Publication 061- 996, N.E.C. Paper. 1963
`
`Fig. 24. Staircase voltage changes with synchronously
`repetitive signal sampling.
`
`12
`
`® Copyright © Tektronix, Inc. All rights reserved. 1/09 SR 85W-23777-0
`
`RPX-Farmwald Ex. 1037, p 15