ELE-6286 RF PROJECT

17.73 MHZ CRYSTAL OSCILLATOR

Submitted By: Prabhat Man Sainju Student Number: 223947 prabhat.sainju@tut.fi 0417077314 December 16, 2011

ii

ABSTRACT TAMPERE UNIVERSITY OF TECHNOLOGY Master’s Degree Programme in Radio Frequency Electronics SAINJU, PRABHAT MAN, 17.73 MHz Crystal Oscillator Project Report, 20 pages December 2011 Subject: ELE-6286 RF Project Examiner: Olli-Pekka Lunden The project Crystal Oscillator was done as the oscillator source for PMR 446 Add-on

Module for FM Receivers.

The design criterion was constrained with the use of crystal oscillator. Unlike the tradi-

tional oscillators based on LC tank circuits, the module had to be based on the crystal.

Crystals are used when the precision is a strict requirement and not a matter of choice.

There are various oscillator design techniques that imply for both crystal and LC tank

oscillators. The report discusses on one of the methods. Simulations for the project are

performed in ADVANCED DESIGN SYSTEM 2009.

iii

TABLE OF CONTENTS

1 INTRODUCTION .................................................................................................... 1

1.1 General Analysis ............................................................................................... 1

1.2 One port Negative Resistance ........................................................................... 2

1.3 Quartz Crystal ................................................................................................... 3

2 DIFFERENT OSCILLATOR CONFIGURATIONS ............................................... 4

2.1 Colpitts/Clapp Oscillator ................................................................................... 4

2.2 Hartley Oscillator .............................................................................................. 6

3 SIMULATIONS ........................................................................................................ 7

3.1 Quartz Crystal Equivalent Model...................................................................... 7

3.2 Specification ...................................................................................................... 7

3.3 Schematic .......................................................................................................... 8

3.4 Transistor Biasing ............................................................................................. 8

3.4.1 Bias Design .......................................................................................... 9

3.4.2 Feedback Capacitors ............................................................................ 9

3.4.3 DC Blocks .......................................................................................... 10

3.5 Simulation Environment ................................................................................. 10

3.6 Transient Analysis ........................................................................................... 10

3.7 Harmonic Analysis .......................................................................................... 11

4 CONSTRUCTION .................................................................................................. 12

5 MEASUREMENT .................................................................................................. 14

5.1 Measured Output ............................................................................................. 15

6 CONCLUSION ....................................................................................................... 16

7 REFERENCE .......................................................................................................... 17

1

1 INTRODUCTION

Quartz crystal oscillators were developed in the 1920s. Prior to the advent of the transis-

tors and monolithic ICs, the oscillators were based on vacuum tubes with operating vol-

tage of staggering 200-300 volts. With transistors, the operating voltage range has gone

much below and the focus on oscillator design is now on the performance and accuracy.

These oscillators are used in most of the communication circuits as the Local Oscillator

source. There are different versions of the oscillator schemes available which shall be

discussed later. All of these oscillators were invented with the use of LC tank as the

primary source of oscillation rather than the quartz crystals. Almost all of the schemes

though are based on the theory of negative resistance. Concept of Negative Resistance

shall be discussed next. The quartz crystal will also be analyzed. After these analyses,

the dots can be connected and seen how the crystal oscillators give rise to stable oscilla-

tion.

1.1 General Analysis

Figure 1.1 Block Diagram of an oscillator with feedback network

Above is the basic block diagram of the feedback network based oscillator. An amplifier

is placed with the gain A and a feedback network with gain of β. is the input

function to the network and is the output function of the network.

We can express the output voltage as,

(1.1)

This can be simplified as,

(1.2)

2

It is evident from the equation 1.2 that for the network to oscillate, the denominator

term should be zero. If it becomes zero, this means that there would be output voltage

even without the input voltage. Now for the denominator to turn zero,

This mandatory condition for the circuit to oscillate is known as Barkhausen Criterion.

Please note that the feedback network β is a frequency dependent term i.e. it is ex-

pressed moreover as β(jω). The criterion states that, if A is the gain of the amplifying

element in the circuit and β(jω) is the transfer function of the feedback path, the circuit

will obtain steady state oscillation only at frequencies for which:

The loop gain is equal to unity in magnitude i.e. .

There must be a positive feedback such that phase shift around the feedback

loop is 0 or integral multiple of 2π. [1]

1.2 One port Negative Resistance

Negative resistance is a conceptual term or better could be termed as a phenomenon that

non linear devices exhibit. The voltage-current slope in such cases tends to extend be-

low the origin as well over a certain region.

Figure 1.2: One port Negative Resistance model

The negative resistance model is represented by the amplitude and frequency dependent imped-

ance given as [2]

Where A is the amplitude of the loop current i(t) and

A passive load is connected to the network given as

3

Using the Barkhausen Criterion, we get

(1.6)

which implies that for the oscillation,

(1.7)

And

(1.8)

The network is unstable if the net resistance of the network is negative; i.e.

Mathematical calculations show that for maximum power delivered to the load network,

the load resistance should be parameterized as below:

Where R0 is the input resistance at A=0.

1.3 Quartz Crystal

A quartz crystal is a small, thin piece of quartz with two opposite surfaces metalized to

make electrical connections. Its physical dimensions are tightly controlled since they

control oscillation frequency. Quartz exhibits a piezoelectric effect, that is, applying a

voltage to the opposing surfaces of a piece of properly oriented quartz will make it

change shape mechanically and vice versa.[3]

Electrical equivalent model of the crystal is given by the figure below:

Figure 1.3 Equivalent Electrical Model of Quartz Crystal

Figure 1.3 depicts the equivalent model of the quartz crystal. R represents the motional

(series) resistance, Cp represents shunt capacitance, C is the series capacitance and L

being the inductance of the device.

4

2 DIFFERENT OSCILLATOR CONFIGURA-

TIONS

Now necessary conditions for the crystal oscillator and the quartz crystal have been in-

troduced, different oscillator configurations those utilize the above to give rise to stable

oscillation need to be discussed.

2.1 Colpitts/Clapp Oscillator

Figure 2.1 Colpitts/Clapp Oscillator with LC tank as oscillator

Above is the Clapp Oscillator configuration. The capacitor network of C1 and C2 is used as

feedback. The only difference between the Colpitts and the Clapp Oscillator is that the extra

capacitor Cr is present. One major setback of the Colpitts Oscillator which is overcome by the

Clapp configuration is the frequency tuning. If either of the capacitors C1 and C2 is changed for

tuning, this could affect the whole feedback network and the circuit might not oscillate

at all.

Let us consider the small signal model of the figure 2.2. Let v1 be the small signal input

voltage, i1 be the small signal input current. Hence the input impedance can be written

as,

5

Since in the Colpitts and Clapp oscillator output is taken from the emitter of the

transistor, the output voltage is equal to

where Z2 is the impedance of the capacitor.

Figure 2.2: Small signal model of the Colpitts Oscillator

Now assuming that the voltage dependent current source delivers the current is we can

find that the total current i2 through the capacitor C2 is given as

But the current supplied by the voltage dependent current source is given as

It is clear from the figure that the current from the current source is the collector current

and the difference of voltage between V1 and V2 is the base-emitter junction voltage.

Now, the input current is given as

Where Z1 is the impedance of the capacitor C1.

Solving with the above results yields to following conclusion:

Thus the input impedance is seen as the sum of impedance of the voltage divider

capacitors C1 and C2 as well as an extra term i.e. the product of their impedances with

the transconductance.

This term can be specified as Rin where

6

Since the impedance of the capacitors are complex, their product yields the negative

value. Hence the Rin is a negative component given as

C1 and C2 form the capacitive feedback network. This network in fact is two capacitors in paral-

lel. Their equivalent capacitance gives the input capacitance of the network as

The frequency of oscillation is given as

For the Clapp Oscillator, one more capacitor Cr is also present which is in parallel to the load

capacitance network. Hence the overall input capacitance becomes

[4]

Efficiency of the oscillator is defined as the ratio of RF power delivered at output to DC power

taken as input.

2.2 Hartley Oscillator

Hartley Oscillator looks similar to Colpitts Oscillator except for that it uses the induc-

tive feedback network instead of capacitive network. The feedback capacitor network is

made by taking a coil and making a tap.

Figure 2.3 Hartley Oscillator [Figure from ADS]

7

3 SIMULATIONS

The Colpitts oscillator was chosen amongst all other option given the design constraints.

Oscillator design was restrained from using the inductors. Hence Colpitts was chosen

over the Hartley configuration.

3.1 Quartz Crystal Equivalent Model

VNA was used to determine the equivalent component values of the quartz crystal. The

measured value was later supplemented to the simulation model to determine the other

component values.

Table 3.1 Quartz Crystal Equivalent Model Parameters

Component Values

Inductance 3 mH (approx)

Motional (Series) Resistance 50 Ohms at max

Series Resistance 21 fF (approx)

Shunt Capacitance 3 to 8 pF

3.2 Specification

Table 3.2 Crystal Oscillator Specification

Item Min Typical Max Unit Notes

Frequency Toler-ance

532.0344

Hz At 25o C

Waveform

Sine wave

Level 3 dBm For 50 ohm load

Harmonics -3 dB Below the fundamental frequency

Input Voltage 5 volts DC Supply

Current 10 mA Current drawn from the source

Size 5 x 5 cm2 Need to fit the design in the given PCB Dimension

8

3.3 Schematic

The schematic for the Colpitts oscillator using the crystal oscillator is similar to that of

the schematic given in figure 2.1. The inductor is replaced by the quartz crystal with one

of the terminals feeding the base of the transistor and the other terminal grounded. The

output is taken from the emitter terminal of the transistor.

Figure 3.1 Schematic of Colpitts Oscillator

5V DC source was used. The crystal used had parameters as described in table 3.1. Sin-

gle resistor biasing has been used as discussed in the theoretical background. One dif-

ferent thing done in the simulation apart from the real construction is the use of the ini-

tial condition. An initial voltage of 1V has been provided at one node of crystal. In reali-

ty, the amplifier uses the internal noise as the startup voltage to be amplified. A capaci-

tor feedback network consisting of two 150 pF capacitors was used.

Oscport is a special device used for an oscillator analysis. For more information, please

refer to the Topics and Index of ADS. I_Probe measures the current at the output.

Mainly two main simulation models were used; Harmonic Balance and Transient Re-

sponse. Harmonic Balance mode was used to analyze the harmonic components in the

output and Transient Analysis to study the real time voltage and current level with re-

spect to time. A harmonic balance could be taken equivalent to analyzing the real circuit

in Spectrum Analyzer and a transient response equivalent to Oscilloscope.

3.4 Transistor Biasing

Simple Collector to base biasing technique has been applied in the schematic. The col-

lector resistance is calculated as

Biasing Network Feedback Network

9

Where Rc is the collector resistance

Vcc is the supply DC voltage

Vc is the collector voltage

Ic is the collector current

The base biasing resistor value can be calculated as,

Where RB is the base resistance indicated in the schematic (Figure 3.1) as R21,

VBE is the Base Emitter forward bias voltage (0.7 V approx.)

RE is the emitter resistance indicated in the schematic ((Figure 3.1) as R23 and

is the current gain of the transistor and is given as

The emitter resistance value RE can be calculated as,

3.4.1 Bias Design

With the above knowledge, the bias network was designed for the given BFP420 tran-

sistor. The parameters given are:

Vcc = +5V

Vc=3.5V

VCE=2 V

Ic=10 mA

=80 approx.

Using equation 3.1, RC=150 Ohms

Using equation 3.3, RE=150 Ohms

Using equation 3.2, RB=10.4K Ohms

3.4.2 Feedback Capacitors

For the feedback capacitor values, equation 2.7 will be referred.

From the equation, if C1=C2

Rin should be equal to the series resistance or the motional resistance of the crystal oscil-

lator.

The transconductance value gm is equal to 0.3 S approx.

Using the equation 3.4, C1=C2=150 pF

10

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0 5.0

-5

0

5

10

-10

15

time, msec

TR

AN

.I_P

robe1.i, m

A

1.5

6815

1.5

6820

1.5

6825

1.5

6830

1.5

6835

1.5

6840

1.5

6845

1.5

6850

1.5

6810

1.5

6855

-5

0

5

10

-10

15

time, msec

TR

AN

.I_P

robe1.i, m

A

3.4.3 DC Blocks

The DC block capacitors have been used in the figure 3.1 at three places; C39 at the

emitter, C40 at the collector feedback and C36 at the DC source. The DC blocks have

been designed to provide minimum impedance for the center frequency while blocking

frequencies below it.

From the impedance of the Capacitor, the capacitance for the specific frequency is given

as

Assuming that the capacitor provides about 10 Ohms of impedance at the center fre-

quency of 17.73 MHz (the expected output of the oscillator), the capacitance value turns

out to be 1nF approx.

3.5 Simulation Environment

As known ADS 2009 was used as the simulation tool and simulated in Windows 64 bit

machine. The major parameters for Harmonic Balance are:

Fundamental Frequency: 17.73 MHz

Order: 3

Oscillator Analysis Method: Use OscPort

The transient analysis parameters are:

Start Time: 0 ns

Stop Time: 5 ms

Step Size: 3 ns (in correspondence with the expected center frequency of 17.73448

MHz)

3.6 Transient Analysis

Figure 3.2 Output Current and Waveform

11

1.9

3252

1.9

3254

1.9

3256

1.9

3258

1.9

3260

1.9

3262

1.9

3264

1.9

3266

1.9

3268

1.9

3270

1.9

3272

1.9

3274

1.9

3250

1.9

3276

-200

0

200

400

-400

600

time, msec

TR

AN

.Vo, m

V

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0 5.0

-200

0

200

400

-400

600

time, msec

TR

AN

.Vo, m

V

5 10 15 20 25 30 35 40 45 500 55

-20

-15

-10

-5

0

-25

5

f req, MHz

dB

m(H

B.V

o)

Readout

m1

Readout

m2

m1freq=plot_vs(dBm(HB.Vo), freq)=2.353745611Max

17.75585301MHz

m2freq=plot_vs(dBm(HB.Vo), freq)=-8.327915817

35.51170602MHz

Pdc

0.045

Pout

0.002

PoutdBm

2.354

Eqn Pout=0.5*real(HB.Vo[1]*conj(HB.I_Probe1.i[1]))

Eqn Pdc=real(-conj(HB.SRC1.i[0])*5)

Eqn PoutdBm=10*log(Pout)+30

Above figure 3.2 shows the current over entire 5 ms time period. It shows that the current

started to grow after 1 ms and at 1.5 ms it attained stable amplitude. The expanded version of

the same waveform is shown in the right side of the figure. This shows that the wave form is not

exactly sinusoidal but with the hint of presence of harmonics.

Figure 3.3 Output Voltage Waveform

Figure 3.3 shows the voltage level at the output. Similar to figure 3.2, the rise of the

oscillation is clearly seen in the figure. The expanded view on the right shows the wave-

form of the output which would have been a pure sinusoid in the absence of harmonics.

Harmonics analysis is done below:

3.7 Harmonic Analysis

Figure 3.4 Harmonic Analysis of the Colpitts Oscillator

Above figure shows the harmonics analysis of the simulated Colpitts Oscillator. The

table above the harmonics figure is generated by ADS. It shows different power levels.

The output power at the fundamental frequency is 2.354 dBm. The power level of 1st

harmonic as per the figure is more than 9 dB below the fundamental frequency. The

second harmonic is much below the fundamental frequency.

12

4 CONSTRUCTION

The layout for the circuit was designed in the ADS Layout Editor. Standard 0603 SMD

components were selected from the ADS Component Library.

Table 4.1 Part list for the layout design

Component Value Part Number Amount

Resistor 150 Ohm CRCW06031500F 2

Resistor 10 kOhm CRCW06031002F 1

Capacitor 150pF C0603C151F5G 2

Capacitor 1 nF C0603C102J5R 3

Crystal 17.73448 MHz - 1

Transistor pb_sms_BFP420_19960901 1

The substrate board used for etching was FR4. Its dielectric constant is 4.5 and thick-

ness of about 0.8 mm. A separate ground plane was also generated to facilitate for the

soldering of the crystal.

The line width was calculated assuming 17.73448 MHz to be center frequency and 50

ohm impedance using the java applet provided in amanogawa web application [5]. The

line width was calculated to be around 43 mils.

Figure 4.1 Layout generated by ADS

Above figure shows the layout generated by the ADS for the oscillator circuit. This

layout was printed on the transparent sheet with high resolution.

The transparent sheet was overlaid on the substrate surface. Then the whole thing in-

cluding the substrate and the transparent film overlaid on the substrate was put in the

ultraviolet exposing machine for about 2 minutes.

The exposed substrate was then taken out and submerged in the diluted solution of

NaOH or the developer solution. Once the layout starts to appear on the surface etched,

the board is washed. It is now ready to be fed to the bubble-tank.

13

Bubble tank contains Sodiumpersulphate, a strong oxidizer that corrodes the un-

necessary copper layer. After 20-25 minutes, the board is ready. [6]

The board is then washed and cleaned with ethanol. A spray of flux is done to the board

so that soldering applied sticks to the board. Holes are then drilled carefully with appro-

priate sized drill bits. The board is now ready for soldering.

Apart from the parts mentioned above, wires were used as the connections to supply and

ground. A SMA connector was used to at the output with the central pin soldered to the

output line and the outer legs soldered to the ground. Figure 4.2 is the image of the final

prototype that was built after the process of etching and soldering the components.

Figure 4.2 Picture of the Crystal Oscillator Prototype

14

5 MEASUREMENT

Figure 5.1 Frequency Response of Prototype 1 in the Spectrum Analyzer

Figure 5.2 Frequency Response of Prototype 2 in Spectrum Analyzer

Mainly two devices have been used during the measurements; they are Oscilloscope and

Spectrum Analyzer. Oscilloscope was used for the analysis of transient response of the

20 25 30 35 40 45 50 5515 60

-60

-40

-20

0

-80

20

freq, MHz

Tra

ce

1

Readout

m1

Readout

m2

m1indep(m1)=plot_vs(Trace1, freq)=4.756

1.779E7m2indep(m2)=plot_vs(Trace1, freq)=1.062

3.553E7

20 25 30 35 40 45 50 5515 60

-60

-40

-20

0

-80

20

p2_prabhat_final..freq, MHz

p2_p

rabh

at_f

inal

..Tra

ce1

17731589.6395.038

m1

Readout

m2

m1indep(m1)=plot_vs(p2_prabhat_final..Trace1, p2_prabhat_final..freq)=5.038

1.773E7

m2indep(m2)=plot_vs(p2_prabhat_final..Trace1, p2_prabhat_final..freq)=1.668

3.546E7

15

oscillator and the spectrum analyzer for the frequency response of the circuit. Spectrum

Analyzer used for this purpose is Agilent E4407B.

The prototype measurements show that both of the prototypes have the power level at the fun-

damental frequency to be above 3 dBm. Also the 1st harmonics is below 3 dB of the fundamen-

tal frequency. The current measurements show that it draws approximately 8.7 mA current from

the source.

5.1 Measured Output

Table 5.1 Measured Output

Parameters Prototype 1 Prototype 2 Unit

Peak-to-Peak Voltage 398 384 mV

Frequency 17.72905 17.72905 MHz

Current drawn from

source 8.71 9.1 mA

Output Power Level 4.75 5.03 dBm (Fundamental Frequency)

1st Harmonics Power

Level 1.06 1.66 dBm

Table 5.1 shows the measurement output in tabulated form. There was no as such Peak-

to-Peak voltage specified for the prototype. But it was just measured out of the oscillos-

cope. All other measurements seem to be meeting the required specifications as com-

pared to the table 3.2. The center frequency observed in the measurement is different

from the expected value as the actual resonance frequency of the crystal was measured

and found to be different from that stated. This was basically due to the feedback capa-

citors that pulled the center frequency down. The frequency tolerance was measured by

changing the span of the spectrum analyzer to 500 Hz. The specified tolerance was 532

Hz. With the frequency span of the analyzer set, the peak was seen to fall within the

span in the scope. This indicates that the frequency tolerance was met.

The current drawn from the source is measured by the digital voltage source. The meas-

ured current was about 8.7 mA approx for first prototype and 9.1 mA for the second

prototype. The measured efficiency using these data is calculated using the equation

2.11.

For prototype 1,

For prototype 2,

16

6 CONCLUSION

Crystal Oscillators are precise and compact oscillators that are used in modern day

communication systems by virtue of its high quality factor and accuracy. The equivalent

model of the quartz crystal shows that it has very high inductance (in the range of mH)

and very low series capacitance (in femtoFarads). These feats are very hard to achieve

with actual components. Even though they might be available, their size may be incom-

parable with that of the commercial quartz crystals. Colpitts Oscillator was originally

designed to be used with the LC tank oscillator. But in this project, it has been used with

the quartz crystal.

For this, the equivalent model of the quartz crystal was observed from VNA. The equiv-

alent model was used in the simulation tool ADS for further simulation. The output was

taken of the emitter and fed to a 50 ohm load. The output measurements presented are

all with respect to 50 ohm load.

The center frequency observed with the measurement was different from that of the

crystal itself. This was because the load capacitance applied in the form of the capacitor

feedback network adds up to the shunt capacitance of the equivalent electrical model of

the crystal. Hence the center frequency is slightly shifted. Though in simulation, we

observed the output power in dBm to be about 2.354 dBm, the hardware measurements

showed it being above 3dBm which was our expectation from the specification.

17

7 REFERENCE

[1] en.wikipedia.org/wiki/barkhausen_stability_criterion

[2] Gonzalez, G. Microwave Transistor Amplifiers Analysis and Design

[3] Robert J. Matthys, CRYSTAL OSCILLATOR CIRCUITS, Revised Edition

[4] en.wikipedia.org/wiki/Colpitts_oscillator

[5] www.amanogawa.com

[6] https://moodle.tut.fi/file.php/1586/PCB_etch.pdf

[7] Pozar, D.M. Microwave Engineering, 3rd Edition