Download COMPUTED ENVELOPE LINEARITY OF SEVERAL FM

COMPUTED ENVELOPE LINEARITY OF SEVERAL
FM BROADCAST ANTENNA ARRAYS
J. Dane Jubera
2008 NAB Engineering Conference
• Complex Envelope Linearity: Ideal is flat amplitude and flat delay
response (vs frequency). Report maximum deviation from ideal.
• Computed Results – No measured data, with apologies.
• Antenna System Analysis
MININECTM for Antenna Z and Radiation Characteristics
all balanced-mode mutual impedances are considered
MathcadTM for offline data reduction and network analysis
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General System Configuration
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“Antennas” and “Transmitters” to be Considered
•
•
•
•
FM Panel Array, 4 bay, 3 faces, Omni, CP
FM Panel Array, as above, with lateral offset & turnstile phasing
Single λ/2 dipole, LP
Resistive Load, non-radiating
• Norton Equivalent Current Source, Zs= 50 Ω
• Norton Equivalent Current Source, Zs= 500 Ω
• Norton Equivalent Current Source, Zs= ∞ Ω
• Linear System Analysis
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iBiquity Digital Corporation HD RadioTM
Specification for Gain and Delay Flatness
“The total gain of the transmission signal path as verified at the
antenna output shall be flat to within ± 0.5 dB for all frequencies
between (Fc – 200 kHz) to (Fc +200 kHz), where Fc is the RF
channel frequency.”
“The differential group delay variation of the entire transmission
signal path (excluding the RF channel) as measured at the RF
channel frequency (Fc ) shall be within 600 ns peak to peak from
(Fc – 200 kHz) to (Fc +200 kHz).”
[1]
Doc. No. SY_SSS_1026s, Rev D, February 18, 2005,
“HD Radio FM Transmission System Specifications”
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Top View of Panel System
Feed Region
Reflector Panel
Dipole
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Isometric View of Panel System
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Top View of Offset Panel System
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Flow Chart for MININECTM Computations
Generate geometry of
radiating structure.
Specify source locations.
Specify source currents – one “on”,
others “off”.
Save configuration file.
Specify frequencies and far field
directions.
Duplicate configuration file for
each source current location.
Modify source currents.
Execute analysis for each
configuration file.
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Flow Chart For Off-line Computations
Collect all port voltage data and construct
antenna port Y matrix at each frequency.
Compute CP mode fields. Compute
delay.
Use network analysis to determine
antenna feed currents when connected
by model feed system.
Collect all far field solutions. Scale by
computed feed currents and superpose.
Display results.
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Results, Configuration 1
Source Impedance:
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50 Ω
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Antenna Input Impedance, Γ Plane
120
90
0.4
60
0.3
150
30
0.2
0.1
Sant
kfreq
180
0
0
210
Antenna Input
 Plane
330
240
300
270
arg Sant
kfreq
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240
300
270
arg Sant
kfreq
Return Loss, Antenna Input
≈ 18 dB over 3.5 MHz
30
25
RLant
Return
Anten
kfreq
20
15
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freq
kfreq
13
Far Field Behavior, Single Channel
Transmitter  "50 Ohm Source"
Azimuth = 0 deg
Δ = 0.05 dB
E_dB 54.95
Lfeed_ft  0
54.9
200
100
0
Freq_kHz
100
200
20
E_Phase
30
40
200
100
0
Freq_kHz
100
200
0.2
_ns
Δ = 0.3 ns
0
0.2
200
100
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0
Freq_kHz
100
200
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Far Field Behavior vs Azimuth, 3 Channels
RIGHT HAND CIRCULAR Polarization
(co-pol)
SourceImpedance  50
Peak-to-peak Delay Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
Worst Case
1
1 
E_RH
ns
2 
E_RH
0.5
Δ = 0.7 ns
3 
E_RH
0
0
45
90
135
180

225
270
315
360
cv
Peak-to-peak Amplitude Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
0.1
 4  0.08
E_RH
5 
E_RH
0.06
dB
6 
E_RH
Δ = 0.09 dB
0.04
0.02
0
45
90
135
180

225
270
315
360
cv
90
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120
EfarRH
3
150
15
60
30
E_RH
dB
6 
E_RH
0.06
0.04
Far Field Behavior vs Azimuth, Magnitude, Polar
0.02
0
45
90
135
180

225
270
315
cv
90
120
EfarRH
3 i
Azimuth Pattern,
Linear Scale
Channels 1, 2, & 3
EfarRH
8 i
60
150
30
180
0
EfarRH
13 i
210
330
240
300
270

i
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Results, Configuration 1
Source Impedance:
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500 Ω
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200 Impedance Presented to Transmitter
Load
200
100
0
100
200
Freq_kHz
≈ 500 ft Transmission Line
Γ Plane
120
kfreq
60
0.4
0.3
0.2
0.1
0
150
Sant
90
0.5
180
30
Input Im
 Plane
0
210
330
240
300
270
arg Sant
kfreq
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Far Field Behavior, Single Channel
Transmitter  "Current Source"
Azimuth = 0 deg
62
E_dB
60
Δ = 1.87 dB
Lfeed_ft  501.75
58
200
100
0
Freq_kHz
100
200
100
E_Phase 50
0
200
100
0
Freq_kHz
100
200
200
_ns
0
Δ = 251 ns
200
200
100
120
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150
90
0.5
0.4
0.3
0.2
0.1
0
Freq_kHz
100
200
60
30
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Input Impedance,
 Plane
Far Field Behavior vs Azimuth, 3 Channels
RIGHT HAND CIRCULAR Polarization
(co-pol)
Lfeed_ft  501.75
SourceImpedance  500
Peak-to-peak Delay Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
Worst Case
260
1 
E_RH
ns
240
2 
E_RH
Δ = 251 ns
 3  220
E_RH
200
0
45
90
135
180

225
270
315
360
cv
Peak-to-peak Amplitude Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
1.9
4 
E_RH
1.8
5 
E_RH
dB
Δ = 1.87 dB
 6  1.7
E_RH
1.6
0
45
90
135
180

225
270
315
360
cv
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Results, Configuration 2
Source Impedance:
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50 Ω
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Antenna Input Impedance, Γ Plane
90
120
60
0.008
0.006
150
30
0.004
0.002
Sant
kfreq
180
0
0
210
Antenna In
 Plane
330
240
300
270
arg Sant
kfreq
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270
arg Sant
kfreq
Return Loss, Antenna Input
60
55
Ret
Ant
50
RLant
kfreq 45
40
35
30
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freq
kfreq
23
Far Field Behavior, Single Channel
Transmitter  "50 Ohm Source"
55.8
E_dB 55.6
Δ = 0.2 dB
55.4
200
100
0
Freq_kHz
100
200
0
Freq_kHz
100
200
45
E_Phase 50
55
200
100
2
_ns
Δ = 2.2 ns
0
2
200
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100
0
Freq_kHz
100
200
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Transmitter  "50 Ohm Source"
RIGHT HAND CIRCULAR Polarization
(co-pol)
Far Field Behavior Vs Azimuth, 3 Channels
Peak-to-peak Delay Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
4
Worst Case
1 
E_RH
ns
2 
E_RH
2
3 
E_RH
Δ = 3.49 ns
0
0
45
90
135
180

225
270
315
360
cv
Peak-to-peak Amplitude Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
0.3
4 
E_RH
0.2
5 
E_RH
dB
Δ = 0.25 dB
 6  0.1
E_RH
0
0
45
90
135
180

225
270
315
360
cv
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EfarRH
3
150
90
25
60
30
dB
 6  0.1
E_RH
0
Far Field Behavior
vs Azimuth,
Magnitude,
Polar 225
0
45
90
135
180
270

cv
90
120
EfarRH
3 i
Azimuth Pattern,
Linear Scale
EfarRH
8 i
60
150
30
180
0
EfarRH
13 i
210
330
240
300
270

i
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Results, Configuration 2
Source Impedance:
500 Ω
≈ 500 ft Transmission Line
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Load Impedance Presented to Transmitter
≈ 500 ft Transmission Line
Γ Plane
90
120
60
0.008
0.006
150
30
0.004
Sant
0.002
kfreq
180
0
0
210
Transmitter Loa
 Plane
330
240
300
270
arg Sant
kfreq
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Far Field Behavior, Single Channel
Transmitter  "Current Source"
61
E_dB 60.8
Δ = 0.31 dB
60.6
200
100
0
Freq_kHz
200
100
0
Freq_kHz
100
200
0
50
E_Phase
100
150
100
200
10
_ns
0
Δ = 11.3 ns
10
200
2008 NAB Engineering Conference
100
0
Freq_kHz
100
200
29
Far Field Behavior vs Azimuth, 3 Channels
Transmitter  "Current Source"
RIGHT HAND CIRCULAR Polarization
(co-pol)
Peak-to-peak Delay Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
Worst Case
15
1 
E_RH
ns
10
2 
E_RH
3 
E_RH
Δ = 11.3 ns
5
0
0
45
90
135
180

225
270
315
360
cv
Peak-to-peak Amplitude Variation across 400 kHz Channel
vs Azimuth
Channels 1, 2, & 3
0.4
4 
E_RH
5 
E_RH
0.2
dB
Δ = 0.31 dB
6 
E_RH
0
0
45
90
135
180

225
270
315
360
cv
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Single Dipole, 98 MHz ± 200 kHz
Source Z
50



Δ Gain
0.04 dB
1.44 dB
0.54 dB
0.30 dB
Δ Delay
Antenna Return Loss
0.01 ns
81 ns
32 ns
19 ns
16.3 dB
16.3 dB
26.4 dB
32.0 dB
• Table above shows performance of a single λ/2 dipole antenna fitted
with a low Q matching circuit with which to adjust impedance.
• Assumed transmission line length is 201 feet. Not as much gain and
delay variation as seen with 500 feet of transmission line.
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Resistive Load, Non-Radiating
•
•
•
•
•
Resistive Load (RL + j 0)
Long Transmission Line, Lossless
Current Source (Zs = )
Evaluate voltage on load resistor vs frequency
ρ=|Γ|, Γ = (RL-Z0)/(RL+Z0)
•
For sufficiently long transmission line (≈ 600’ @ FM)
Δt = 4ρ(L/v)/(1- ρ2)
ΔG = 20 log(VSWR) = 20 log [(1+ρ)/(1-ρ)]
(L/v is 1-way transit time in transmission line)
•
Example 1: For ρ=0.2, L/v = 720 ns ( ≈ 700 ft) =>
Δt = 600 ns & ΔG = 3.5 dB
Example 2: For ρ=0.126 (18 dB RL), L/v = 508 ns ( ≈ 500 ft) =>
Δt = 260 ns & ΔG = 2.2 dB
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Summary of Results
System
Array 1
Array 1
Array 2
Array 2
Single Dipole
Single Dipole
Resistor
•
•
•
Return Loss
18 dB
18 dB
40+ dB
40+ dB
16 dB
16 dB
14 dB
Source
Impedance
50
500
50
500
50
inf.
inf.
Transmission
Variation,
Line Length (nom) Amplitude(dB)
500'
0.09
500'
1.87
500'
0.25
500'
0.31
200'
0.04
200'
1.44
680'
3.52
Variation,
Delay (ns)
0.7
251
3.49
11.3
0.01
81
600
Contribution to envelope non-linearity is primarily via the antenna input mismatch,
length of transmission line, and transmitter source mismatch.
Systems using transmitters which are source matched to the transmission line
show very good performance in all cases studied here relative to HD Radio
specification of 1 dB gain variation and 600 ns delay variation.
Systems using transmitters with high VSWR relative to line impedance require
low antenna VSWR to achieve similar envelope linearity performance.
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