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RISC-division
Aalborg University, Department of Communication Technology
Niels Jernes Vej 12 – A6, DK-9220 Aalborg East
RISC8-1-TCMT-mm9/05
1/2
050330/OKJ
rev. 060306/OKJ
Transceiver Components and Measuring Techniques, mm9
Suggested solutions
1.
A receiver is required to pass a blocking test with a –39 dBm CW-blocker at an offset of 600 kHz
from the desired channel. The reference (desired) signal level is –99 dBm, the detection SNR is 9
dB and the channel bandwidth is 200 kHz. What is the required phase noise spectral density of the
local oscillator signal at 600 kHz offset? Approximation: Assume that the LO phase noise spectrum
is flat from 500 kHz to 700 kHz offset.
=
=
=
Reference signal level
Required S/N-ratio
Allowed disturbance level (in 200 kHz bandwidth)
Bandwidth = 200 kHz (Approximation: Flat spectrum over 200 kHz band)
Allowed disturbance level in 1 Hz bandwidth
Blocker (=carrier) level
L(600 kHz) = Allowed noise spectral density relative to carrier
or another way around:
Reference signal level
- Required S/N-ratio
= Allowed disturbance level (in 200 kHz bandwidth)
- Blocker level
= Disturbance level relative to blocker level
= Allowed oscillator noise relative to carrier (in 200 kHz bandwidth)
- Bandwidth = 200 kHz (Approximation: Flat spectrum over 200 kHz band)
= L(600 kHz) = Allowed noise spectral density relative to carrier
-99
9
-108
53
-161
-39
-122
-99
9
-108
-39
-69
dBm
dB
dBm
dBHz
dBm/Hz
dBm
dBc/Hz
dBm
dB
dBm
dBm
dBc
53 dBHz
-122 dBc/Hz
Note: This calculation does not include other noise and distortion products which may degrade the
BER.
2.
A single loop PLL has an offset in the loop filter corresponding to a phase offset, Δθ, of 0.01 rad
(0.57Ε). The loop parameters are:
N = 1000
Loop division ratio.
fref = 100 kHz Reference frequency (at phase detector).
Loop natural frequency.
fn = 1 kHz
ϕ = 53o
Loop phase margin.
a. Calculate the relative level of the spurious signal at 1st and 2nd harmonic of the reference frequency.
Use (the reformulated) results from “Brennan” for a 3rd order loop with a phase-frequency detector
for relative levels of the sidebands at ω0 ± nωref :
Ole Kiel Jensen, [email protected], Telephone +45 9635 8663
RISC-division
Aalborg University, Department of Communication Technology
Niels Jernes Vej 12 – A6, DK-9220 Aalborg East
SideBand relative, voltage ( n ⋅ ω ref ) =
(
2/2
2 ⎛ Δθ ⎞
sin⎜ n
⎟ ⋅ H closedloop ( n ⋅ ω ref )
n ⎝ 2 ⎠
N ⋅ ω n2 (tg (ϕ ) + 1 / cos(ϕ )) s + ω n3
)
H closedloop ( s ) = 3
s + ω n ( tg (ϕ ) + 1 / cos(ϕ )) s 2 + ω n2 ( tg (ϕ ) + 1 / cos(ϕ )) s + ω n3
H closedloop ( nω ref >> ω n ) ≈
N ⋅ ω n2 (tg (ϕ ) + 1 / cos(ϕ ))
2
n 2ω ref
b. Calculate the settling time to 2% frequency error for a frequency step using “Brennan” fig. 7.6
or (7.22):
ω Error (t ) = Δω [1 + ω nt − (ω nt )2 ]e−ω
nt
a.
Approximation: fref >> fn
H closedloop ( nω ref >> ω n ) ≈
n=1
n=2
0.299
0.0747
2.99Α10-3
~ -50.5 dB
747Α10-6
~ -62.5 dB
N ⋅ ω n2 (tg (ϕ ) + 1 / cos(ϕ ))
2
n 2ω ref
SideBand relative, voltage ( n ⋅ ω ref ) =
2 ⎛ Δθ ⎞
sin⎜ n
⎟ ⋅ H closedloop ( n ⋅ ω ref )
n ⎝ 2 ⎠
b.
Reading from Figure 7.6: ωnt . 9
Solving:
ω Error (t ) = Δω [1 + ω nt − (ω nt )2 ]e−ω t
n
gives by iteration ωnt ∼= 7.9
tSettling = 7.9/ωn =
1.26 ms
Ole Kiel Jensen, [email protected], Telephone +45 9635 8663
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