Report on Voltage Control

Oscillator and Phase Lock Loop

Nguyen Quang Hai

June 10, 2015

Contents

1 Introduction 1

2 Voltage Control Oscillator (VCO) 2

2.1 Colpitts oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Control the frequency by diode capacitor . . . . . . . . . . . . . . . . . . . . 3

3 Comparision between the new and the old circuit 7

3.1 Phase Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Low pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3 Voltage control oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Phase lock loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Result of the new circuit only 13

4.1 Phase Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2 Low pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.3 Voltage control oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.4 Phase lock loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Circuit schematic 19

5.1 Phase detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.2 Low pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.3 VCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

i

5.4 Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.5 BNC connector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.6 Additional components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

ii

Chapter 1

Introduction

This report discusses the making of the voltage control oscillator (vco) and the comparision

between the new and the old circuit.

1

Chapter 2

Voltage Control Oscillator (VCO)

2.1 Colpitts oscillator

The main part of the VCO is the oscillator, and in this circuit, Colpitts oscillator is used.

Figure 2.1: Colpitts Oscillator

Figure 2.1 shows the basic configuration of the Colpitts oscillator. Resistors RB, RC are used

to bias the transistor. The resonance frequency of this oscillator can be found by:

2

f0 =1

2π√L1C

(2.1)

And the capicitance C can be calculated by the following formula:

C =C2C4

C2 + C4

=1nF · 10nF

1nF + 10nF= 0.91nF (2.2)

Then the resonance frequency can be found as follow:

f0 =1

2π√L1C

=1

2π√

12.6uH · 0.91nF= 1.486MHz (2.3)

To control the frequency of this circuit, diode capacitor is used. The realization of this circuit

is discussed in the next section.

2.2 Control the frequency by diode capacitor

Figure 2.2 shows the schematic of the VCO. From the previous section, the resonance fre-

quency of this circuit can be calculated as following:

f0 =1

2π√L1Ctot

(2.4)

And Ctot can be described as: Ctot = C4 series (C2 // (C1 series n× Cd)) (n is the number

of diode capacitance).

3

Figure 2.2: Circuit schematic of VCO

From the circuit description, Ctot can be obtained as following:

Ctot =20nCdC1 + C2

1

12nCd + 11C1

(2.5)

C1 = C2 = 110C4 is used for simplification and Cd is the capacitance of the diode capacitor.

And the number of used diode capacitors can be derived as following:

n =11C1Ctot − 10C2

1

20Cd − 12CdC1

(2.6)

From formula 2.4, to obtain the frequency of f = 1.37MHz, Ctot must be equal 1.0711 nF.

From Formula 2.6 and from Figure 2.3, the number of diode needed at the reversed voltage

Ust = 6V is n = 7.

4

Figure 2.3: Diode capacitance as the function of reserved voltage

Figure 2.4 and Table 2.1 show the result of measurement of the VCO. It can be seen that f

is equal 1.37 MHz at Ust is approximately at 2.5V not at 6V as the calculation above. This

result will be used to evaluate the behavior of the phase look loop.

5

Table 2.1: Measured resonance frequency

Ust f/MHz0 1.322 1.364 1.406 1.428 1.4410 1.4512 1.4614 1.4716 1.47

Figure 2.4: Static modulation characteristic of the VCO

6

Chapter 3

Comparision between the new and the

old circuit

3.1 Phase Detector

Table 3.1 and Figure 3.1 show the comparision between the old and the new circuit. There is

little difference between two curves, eventhough the old circuit works at the input frenquency

of 1.38 MHz meanwhile the new one operates at 1.37 Mhz. The important point is that, at

90 degree, the output voltage of the new circuit is 0V, which satifies the requirement.

7

Table 3.1: Transfer function of phase detector

Phase/degree Uout/V original Uout/V new0 0.57 0.5710 0.56 0.5620 0.54 0.5330 0.50 0.4940 0.44 0.4450 0.37 0.3860 0.30 0.2970 0.20 0.2080 0.11 0.1090 0.01 0.00100 -0.08 -0.10110 -0.18 -0.18120 -0.27 -0.27130 -0.35 -0.35140 -0.42 -0.42150 -0.47 -0.46160 -0.52 -0.52170 -0.54 -0.54180 -0.55 -0.55

Figure 3.1: Transfer function of phase detector

8

3.2 Low pass filter

In this part, the transfer function of the new and the old low pass filter are compared. From

Figure 3.2, the cut off frequency of the old circuit fc equals 260kHz and the new one’s is 300

kHz.

Table 3.2: Transfer function of low pass filter

f/Hz Uout,rms/mV original Damping/dB original Uout,rms/mV new Damping/dB new10 1000 20 1000 2020 1000 20 1000 2050 1000 20 1000 20100 1000 20 1000 20200 1000 20 1000 20500 1000 20 1000 201k 1000 20 1000 202k 1000 20 1000 205k 1000 20 1000 2010k 1000 20 990 19.920k 1000 20 980 19.850k 960 19.7 960 19.6100k 920 19.3 920 19.3200k 810 18.2 820 18.3500k 490 13.8 580 15.3800k 290 9.3 280 8.9

1,000k 200 6.0 160 4.0

9

Figure 3.2: Transfer function of low pass filter

3.3 Voltage control oscillator

From the old circuit, the modulation characteristic is linearised at operation point Ust = 6V

and the constant k0 has the result:

k0 =∆ω

∆Ust

=2π∆f

∆Ust

=2π × 0.04Mhz

4V= 2π × 104rad/V s (3.1)

For the new circuit, the modulation characteristic is linearised at operation point Ust = 2V

and the constant k0 has the result:

k0 =∆ω

∆Ust

=2π∆f

∆Ust

=2π × 0.08Mhz

4V= 4π × 104rad/V s (3.2)

10

Table 3.3: Static modulation characteristic of the VCO

Ust f/MHz original f/MHz new0 1.30 1.322 1.33 1.364 1.36 1.406 1.38 1.428 1.40 1.4410 1.41 1.4512 1.42 1.4614 1.42 1.4716 1.43 1.47

Figure 3.3: Static modualation characteristic of the VCO

11

3.4 Phase lock loop

This section shows the result of the closed control loop. The center frequency of the new

circuit is fc = 1.37MHz and it has a better Lock range and Capture range than the old one.

Table 3.4: Result of the closed control loop

Original circuit New circuitfOH/MHz 1.408 1.427fUH/MHz 1.388 1.378fUL/MHz 1.371 1.358fOL/MHz 1.334 1.311

Lock range/KHz 74 116Capture range/KHz 17 20

12

Chapter 4

Result of the new circuit only

4.1 Phase Detector

• Set amplitude of 2 generators to Uss1 = 4V, Uss2 = 8V .

• Frequency of both signal is set to 1.37MHz.

The constant kD of the phase detector:

kD =∆Uout

∆Φ=

0.37V − (−0.35V )130−50180

× πrad= 0.516V/rad (4.1)

13

Table 4.1: Transfer function of phase detector

Phase/degree Uout/V0 0.5710 0.5620 0.5330 0.4940 0.4450 0.3860 0.2970 0.2080 0.1090 0.00100 -0.10110 -0.18120 -0.27130 -0.35140 -0.42150 -0.46160 -0.52170 -0.54180 -0.55

Figure 4.1: Transfer function of phase detectorr

14

4.2 Low pass filter

• Changing the input frequency from 10Hz to 1MHz while keeping the amplitude con-

stant at Urms = 100mV .

• The cut off frequency of the low pass filter is fg = 300kHz.

Table 4.2: Transfer function of low pass filter

f/Hz Uout,rms/mV Damping/dB10 1000 2020 1000 2050 1000 20100 1000 20200 1000 20500 1000 201k 1000 202k 1000 205k 1000 2010k 990 19.920k 980 19.850k 960 19.6100k 920 19.3200k 820 18.3500k 580 15.3800k 280 8.9

1,000k 160 4.0

15

Figure 4.2: Transfer function of low pass filte

4.3 Voltage control oscillator

• Adjust Ust from 0V to 16V, draw the transfer function.

• Linearise at operation point Ust = 2V and determine constant k0.

The result of k0:

k0 =∆ω

∆Ust

=2π∆f

∆Ust

=2π × 0.08Mhz

4V= 4π × 104rad/V s (4.2)

16

Table 4.3: Static modulation characteristic of the VCO

Ust f/MHz0 1.322 1.364 1.406 1.428 1.4410 1.4512 1.4614 1.4716 1.47

Figure 4.3: Static modualation characteristic of the VCO

4.4 Phase lock loop

Adjust the input signal to f = 1.37MHz and U = 4V. Table 4.4 shows the result of the

measusement.

17

Table 4.4: Result of the closed control loop

New circuitfOH/MHz 1.427fUH/MHz 1.378fUL/MHz 1.358fOL/MHz 1.311

Lock range/KHz 116Capture range/KHz 20

18

Chapter 5

Circuit schematic

5.1 Phase detector

Figure 5.1: Schematic of phase detector

19

Figure 5.2: Layout of phase detector

20

5.2 Low pass filter

Figure 5.3: Schematic of low pass filter

Figure 5.4: Layout of low pass filter

21

5.3 VCO

Figure 5.5: Schematic of VCO

Figure 5.6: Layout of the board

22

5.4 Board

Figure 5.7: Layout of the board

Figure 5.8: Picture of the board

23

5.5 BNC connector

MUILTICOMP 13-22 Buchse Flansch BNC 50 OHM

Bestellnummer: 1169700 from de.farnell.com

Figure 5.9: BNC connector

24

5.6 Additional components

Figure 5.10: Additional components

• 1: C = 1µF

• 2: C = 22pF,R = 10MΩ

• 3: C = 100nF,R = 5.1kΩ

25