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PHYSICS MATHEMATICS AND ASTRONOMY DIVISION

CALIFORNIA INSTITUTE OF TECHNOLOGY

Freshman Physics Laboratory

Instrumentation:The CRT Oscilloscope

Copyright c Virgnio de Oliveira Sannibale, 2001

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Contents

A The Cathode Ray Tube Oscilloscope 5A.1 The Cathode Ray Tube Oscilloscope . . . . . . . . . . . . . . 5

A.1.1 The Cathode Ray Tube . . . . . . . . . . . . . . . . . . 5A.1.2 The Horizontal and Vertical Inputs . . . . . . . . . . 7A.1.3 The Time base Generator . . . . . . . . . . . . . . . . 8A.1.4 The Trigger . . . . . . . . . . . . . . . . . . . . . . . . 8

A.2 Oscilloscope Input Impedance . . . . . . . . . . . . . . . . . . 9A.3 Oscilloscope Probe . . . . . . . . . . . . . . . . . . . . . . . . 9

A.3.1 Probe Frequency Compensation . . . . . . . . . . . . 11A.4 Beam Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . 14

A.4.1 CRT Frequency Limit . . . . . . . . . . . . . . . . . . . 15

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4 CONTENTS

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Appendix A

The Cathode Ray TubeOscilloscope

A.1 The Cathode Ray Tube OscilloscopeThe cathode ray tube oscilloscopeis essentially an analog 1 instrument that isable to measure time varying electric signals. It is made of the followingfunctional parts (see gure A.1):

the cathode ray tube (CRT),

the trigger, the horizontal input,

the vertical input,

time base generator.

Lets study in more detail each component of the oscilloscope.

A.1.1 The Cathode Ray Tube

The CRT is a vacuum envelope hosting a device called electron gun , ca-pable of producing an electron beam, whose transverse position can bemodulated by two electric signals (see gures A.1 and A.7).

1 Hybrid instruments combining the characteristics of digital and analog oscilloscopes,with a CRT, are also commercially available.

5

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6 APPENDIX A. THE CATHODE RAY TUBE OSCILLOSCOPE

When the electron gun cathode is heated by a wire resistance, because

of the Joule effect it emits electrons . The increasing voltage differencesbetween a set of shaped anodes and the cathode accelerates electrons to aterminal velocity v0 creating the so called electron beam.

RampGenerator

CATODE RAY TUBE (CRT)

V/div

Preamplifier Amplifier

INPUT CHANNEL

TRIGGER

Line(60Hz)

External

Internal

LevelSource s/div

TIME BASE GENERATOR

Figure A.1: Oscilloscope functional schematics

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A.1. THE CATHODE RAY TUBE OSCILLOSCOPE 7

The beam then goes through two orthogonally mounted pairs of metal-

lic plates. Applying a voltage difference to those platesV

x andV

y , thebeamis deected along two orthogonal directions (x and y ) perpendicular to itsdirection z. The deected electrons will hit a plane screen perpendicu-lar to the beam and coated with orescent layer. The electrons interactionwith this layer generates photons, making the beam position visible on thescreen.

Sawtoothsignal

v (t)y

t

t

t

T T

Trigger

Figure A.2: Periodic Signal triggering.

A.1.2 The Horizontal and Vertical Inputs

The vertical and horizontal plates are independently driven by a variable

gain amplier to adapt the signals vx (t), and vy (t) to the screen range. ADC offset can be added to each input to position the signals on the screen.These two channels used to drive the signals to the plates signals are calledhorizontal and vertical inputs of the oscilloscope.

In this conguration the oscilloscope is indeed an x-y plotter.

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C 0

C s R s DeflectionPlates

AmplifierHigh VoltageGND

AC

DC

Input

PreAmplifier

Figure A.3: Oscilloscope input impedance representation using ideal com-ponents (gray box). Input channel coupling is also shown.

A.1.3 The Time base Generator

If we apply a sawtooth signal V x (t) = t to the horizontal input, the hori-zontal screen axis will be proportional to time t . In this case a signal vy (t)applied to the vertical input, will depict on the oscilloscope screen the sig-nal time evolution.

The internal ramp signal is generated by the instrument, with an am-plication stage that allows changes in the gain factor and in turn theinterval of time shown on the screen. This amplication stage and the

ramp generator are called the time base generator.In this conguration, the horizontal input is used as a second indepen-

dent vertical input, allowing the plot of the time evolution of two signals.Visualization of signal time evolution is the most common use of an

oscilloscope.

A.1.4 The Trigger

To study a periodic signal v(t) with the oscilloscope, it is necessary to syn-

chronize the horizontal ramp V x = t with the signal to obtain a steadyplot of the periodic signal. The trigger is the electronic circuit which pro-vides this function. Lets qualitatively explain its behavior.

The trigger circuit compares v(t) with a constant value and produces apulse every time the two values are equal and have the same slope sign.

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A.2. OSCILLOSCOPE INPUT IMPEDANCE 9

The rst pulse triggers the start of the sawtooth signal of period 2 T , which

will linearly increase until it reaches the valueV

=T

, and then is reset tozero. During this time, the pulses are ignored and the signal v(t) is indeedplotted for a duration time T. After this time, the next pulse that triggersthe sawtooth signal will happen for the same previous value and slopesign of v(t), and the same portion of the signal will be re-plotted on thescreen.

A.2 Oscilloscope Input ImpedanceA good approximation of the input impedance of the oscilloscope is shown

in the circuit of gure A.3. The different input coupling modes ( DC ACGND ) are also represented in the circuit.The amplifying stage is modeled using an ideal amplier (innite in-

put impedance) with a resistor and a capacitor in parallel to the amplierinput.

The switch allows to ground the amplier input and indeed to verti-cally set the origin of the input signal (GND position), to directly couplethe input signal (DC position), or to mainly remove the DC component of the input signal (AC position).

A.3 Oscilloscope ProbeAn oscilloscope probe is a device specically designed to minimize the ca-pacitive and resistive load added to a circuit under measurement once theinstrument is connected to the circuit. The price to pay is an attenuationof the signal that reaches the oscilloscope input 3 .

Lets analyze the behavior of a passive probe. Figure A.4 shows theschematics of the equivalent circuit of a passive probe and of the inputstage of an oscilloscope. The capacitance of the probe cable can be consid-ered included in C s

Considering the voltage divider equation, we have

H (j ) =V sV i

=Z s

Z p + Z s, (A.1)

2 In general, the sawtooth signal period T and the period of v (t ) are not equal.3 Active probes can partially avoid this problems by amplifying the signal.

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C p

Rp

CableCoaxial

C s

V s

Rs

Oscilloscope Input Stage

Rp

Rs

V i

C p

C s

V s

Probe

Probe Tip

GND Clip

BA

Figure A.4: Oscilloscope input stage and passive probe schematics.Theequivalent circuit made of ideal components for the probe shielded cableis not shown.

where1

Z s= jC s +

1R s

,1

Z p= jC p +

1R p

,

and thenZ s =

R sj s + 1

, Z p =R p

j p + 1.

Dening the following parameters

p = C pR p , =R s

R s + R p, =

C pC s + C p

,

and after some tedious algebra, equation (A.1) becomes

H (j ) = 1 + j p

1 + j p,

which is the transfer function from the probe input to the oscilloscope in-put before the ideal amplication stage.The DC and high frequency gain of the transfer function H (j ) are

respectivelyH (0) = , H ( ) = .

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A.3. OSCILLOSCOPE PROBE 11

Frequency

Phase

Magnitude

2

1

Figure A.5: Qualitative transfer function from the under compensatedprobe input to the oscilloscope input before the ideal amplication stage.As usual, the oscilloscope input is described having an impedance R s || C s .

The numerator and denominator of H (j ) are respectively equal tozero, (the zeros and poles of H ) when

= z = j1 p

, = p = j

1 p

.

Figure A.5 shows the qualitative behavior of H for > 1.

A.3.1 Probe Frequency Compensation

By tuning the variable capacitor C p of the probe, we can have three possi-ble cases

< 1 over-compensation

= 1 compensation

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> 1 under-compensation

if < the transfer function attenuates more at frequencies above z ,and the input signal V i is distorted.

if = the transfer function is constant and the input signal V i will beundistorted, and attenuated by a factor .

if > the transfer function attenuates more at frequencies below pand the input signal V i is distorted.

The ideal case is indeed the compensated case, because we will haveincreased the input impedance by a factor without distorting the signal.

The probe compensation can be tuned using a signal, which shows aclear distortion when it is ltered. A square wave signal is very useful inthis case because, it shows a different distortion if the probe is under orover compensated. Figure A.6 sketches the expected square wave distor-tion for the two un-compensated cases.

It is worthwhile to notices that

= 1 , R sR p

=C pC s

.

This condition implies that:

the voltage difference V 1 across R s is equal the voltage difference V 2across C s , i.e V 1 = V 2

the voltage difference V 3 across R p is equal the voltage difference V 4across C p , i.e. V 3 = V 4

and indeed V 1 + V 2 = V 3 + V 4 .

This means that no current is owing through the branch AB, and we canconsider just the resistive branch of the circuit to calculate V s . Applyingthe voltage divider equation, we nally get

V s =R s

R s + RV i

The capacitance of the oscilloscope does not affect the oscilloscope in-put anymore, and the oscilloscope + probe input impedance R i becomesgreater, i.e.

R i = R s + R p .

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A.3. OSCILLOSCOPE PROBE 13

t t

V V

Figure A.6: Compensation of a passive probe using a square wave. Leftgure shows an over compensated probe, where the low frequency con-tent of the signal is attenuated. Right gure shows the under compensatedcase, where the high frequency content is attenuated.

yV

0v

yE

d D

0V x

h z

e

Figure A.7: CRT tube schematics. The electron enters into the electric eld

and makes a parabolic trajectory. After passing the electric eld region itwill have a vertical offset and deection angle .

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A.4 Beam TrajectoryLets consider the electron motion through one pair of plates.

The electron terminal velocity v0 coming out from the gun can be easilycalculated considering that its initial potential energy is entirely convertedinto kinetic energy, i.e

12

v 20 = eV 0 , v0 = 2eV 0 ,where is the electron mass, e the electron charge, and V 0 the voltageapplied to the last anode.

If we apply a voltage V y to the plates whose distance is h , the electronswill feel a force F y = eE y due to an electric eld

|E y | =V yh

.

The equation of dynamics of the electron inside the plates is

z = 0 , z = v0 ,y = e|E y | .

Supposing that V y is constant, the solution of the equation of motionwill be

z(t) = 2eV 0 t,y(t) =

12

eV yh

t 2 .

Removing the dependency on the time t , we will obtain the electronbeam trajectory , i.e.

y =1

4hV yV 0 z

2

,

which is a parabolic trajectory.Considering that the electron is transversely accelerated until z = d,

the total angular deection will be

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A.4. BEAM TRAJECTORY 15

tan = yz z = d

= 12

dh

V yV 0

.

and displacement Y on the screen is

Y (V y ) = y(z = d) + tan D,

i.e.,Y (V y ) =

12

dh

1V 0

(d2

+ D )V y .

Y is indeed proportional to the voltage applied to the plates through arather complicated proportional factor.

The geometrical and electrical parameters of this proportional factorplay a fundamental role in the resolution of the instrument. In fact, thesmaller the distance h between the plates, or the smaller the gun voltagedrop V 0 , the larger is the displacement Y . Moreover, Y increases quadrat-ically with the electron beam distance d.

A.4.1 CRT Frequency LimitThe electron transit time through the plates determine the maximum fre-

quency that a CRT can plot. In fact, if the transit time is much smallerthan the period T of the wave form V (t), we have

V (t) constant , if T,

and the signal is not distorted.The transit time is

=dv0

= d 2eV 0 .Supposing that

V 0 = 1kVd = 20mmc2 0.5MeVe = 1eV

1ns

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