exercise task 1

7/28/2019 Exercise Task 1

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Chair of Integrated Analog Circuitsand RF Systems

Exercises for the lecture RF Systems

Contact person: Iyappan [email protected] 80 20154Walter-Schottky-Haus, Sommerfeldstr. 24, 3. Stock, Flur C

1 Modulation

Figure 1 shows a Bluetooth spectrum.

Att 5 dB*

*RBW 5 kHz

SWT 170 ms

*VBW 300 Hz

Ref -20 dBm

Center 2.44 GHz Span 5 MHz500 kHz/

*

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

1

Marker 1 [T1]

-45.48 dBm

2.44 GHz

Figure 1: Bluetooth spectrum.

1.1. Calculate the 3 dB, 20 dB and 60 dB bandwidth of the spectrum depicted infigure 1.

1.2. Calculate the bandwidth efficiency for the following signals:

(a) 3 MBit/s mode Bluetooth (bandwidth 1 MHz)

(b) 1 MBit/s mode Bluetooth (20 dB bandwidth from exercise )

(c) 1 MBit/s mode Bluetooth Low Energy (20 dB bandwidth out of figure 2)

Exercises RF Systems - WS 2012 -




Att 5 dB *

* R BW 5 k Hz

S WT 1 70 m s

* V BW 3 00 H z

*Ref -20 dBm

Center 2.44 GHz Span 5 MHz500 kHz/

-120

-110

-100

-9 0

-8 0

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

1

T1 T2

M ar ke r 1 [ T1 ]

-47.31 dBm

2.440008013 GHz

n dB [ T1 ] 2 0. 00 d B

BW 1.161858974 MHz

T em p 1 [ T1 n dB ]

-67.37 dBm

2.439423077 GHz

T em p 2 [ T1 n dB ]

-67.62 dBm

2.440584936 GHz

Figure 2: Bluetooth Low Energy spectrum.





1.3. Calculate the phase of the QPSK and DQPSK signal for the given bit sequence intable 2 and plot phase and phase transitions in the given constellation diagrams.

Signal Bit QPSK Phase DQPSK Phase Transition0 00 +45 +45

1 01 +135 +135

2 10 +225 -135

3 11 +315 -45

Table 1: Phase Coding.

Signal Bit QPSK Phase DQPSK Phase

- - 0

0

031010

Table 2: Phase values.

Q(t)

I(t)0.5 1-0.5-1

-0.5

-1

0.5

1

(a) Constellation Diagram QPSK.

Q(t)

I(t)1-1

-1

1

(b) Constellation Diagram DQPSK.





1.4. Plot the timedomain waveforms of a MSK and ASK signal for the given bit se-quence and calculate the energy of both signals (integral of signal).

• Bit sequence: 11010010

• 1 : 1 V

• 0 : 0 V

• R=1 Ω

• T s = 50 µ s

• MSK

– Amplitude= 1 V

– Frequency for signal = 0 f 1 = 20 kHz

– Frequency for signal = 1 f 2 = ?

• ASK

– Amplitude= 1 V

– Carrier frequency f c = 20 kHz





0 50 100 150 200 250 300 350 400-1

-0.5

0

0.5

1

Time [s]

O u t p u t [ V

]

Figure 3: Baseband signal.

0 50 100 150 200 250 300 350 400-1

-0.5

0

0.5

1

Time [s]

O u t p u t [ V ]

Figure 4: ASK signal.

0 50 100 150 200 250 300 350 400-1

-0.5

0

0.5

1

Time [s]

O u t p u t [ V ]

Figure 5: MSK signal.





Figure 6 shows the construction of an eye diagram.

Break the waveform

into two Symbol time

Sections (length 2TS)

Overlay each section

onto the same time axis

“Eye” Diagram

Time

A m p l i t u d e

Time

A m p l i t u d e

Figure 6: Explanation for eye diagram.

Eye diagrams are useful tools to measure different signal properties. They are verycommon for high speed data links. In figure 7 several signal parameters which canbe measured out of an eye diagram are shown.

• DA is a measure for the amount of distortion at sampling instant and isrelated to signal SNR.

• M N characterizes which amount of noise can be tolerated by the signal.

• J T is a measure for the timing jitter.

• The time over which a successfully sampling is possible is called S T and isequal to the opening of the eye.

A good signal has a wide open eye diagram which is equal to a large M N and S T .

1.5. Quantify DA, M N , J T and S T out of the given eye diagrams in figure 8 and 9.





0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-1

-0.5

0

0.5

1

Symbol Time Intervals

D A

S T

Optimum sampling time

J T

M N

Figure 7: Legend eye diagram.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-1

-

0

0.5

1

Symbol Time Intervals

0.5 A m p

l i t u d e [ V ]

Figure 8: Eye diagram 1.





0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-1

-0.5

0

0.5

1

Symbol Time intervals

A

m p l i t u d e [ V ]

Figure 9: Eye diagram 2.


exercise task 1

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