computed envelope linearity of several fm broadcast antenna arrays j. dane jubera 2008 nab...

COMPUTED ENVELOPE LINEARITY OF SEVERAL FM BROADCAST ANTENNA ARRAYS

J. Dane Jubera

2008 NAB Engineering Conference

2008 NAB Engineering Conference 2

• 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


General System Configuration


“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


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”


Top View of Panel System

Reflector Panel

Dipole

Feed Region


Isometric View of Panel System


Top View of Offset Panel System


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.


Flow Chart For Off-line Computations

Collect all port voltage data and construct antenna port Y matrix at each frequency.

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.

Compute CP mode fields. Compute delay.

Display results.


Results, Configuration 1

Source Impedance: 50 Ω


Santkfreq

arg Santkfreq

0

30

60

90

120

150

180

210

240

270

300

330

0.4

0.3

0.2

0.1

0

Antenna Input Match, Plane

RLantkfreq

freqkfreq

15

20

25

30

Return Loss,Antenna Input

Antenna Input Impedance, Γ Plane


Santkfreq

arg Santkfreq

0

30

60

90

120

150

180

210

240

270

300

330

0.4

0.3

0.2

0.1

0

Antenna Input Match, Plane

RLantkfreq

freqkfreq

15

20

25

30


≈ 18 dB over 3.5 MHz

Return Loss, Antenna Input


Far Field Behavior, Single ChannelTransmitter "50 Ohm Source" Azimuth = 0 deg

E_dB

Freq_kHz200 100 0 100 200

54.9

54.95

Lfeed_ft 0

E_Phase

Freq_kHz200 100 0 100 200

40

30

20

_ns

Freq_kHz200 100 0 100 200

0.2

0

0.2

Δ = 0.05 dB

Δ = 0.3 ns


Far Field Behavior vs Azimuth, 3 ChannelsRIGHT HAND CIRCULAR Polarization(co-pol)

SourceImpedance 50 Peak-to-peak Delay Variation across 400 kHz Channel vs Azimuth

Channels 1, 2, & 3

E_RH1

E_RH2

E_RH3

cv

0 45 90 135 180 225 270 315 3600

0.5

1

ns

Peak-to-peak Amplitude Variation across 400 kHz Channel vs Azimuth

Channels 1, 2, & 3

E_RH4

E_RH5

E_RH6

cv

0 45 90 135 180 225 270 315 3600.02

0.04

0.06

0.08

0.1

dB

EfarRH3 i

EfarRH8 i

EfarRH13 i

i

0

30

6090

120

150

180

210

240270

300

330

Azimuth Pattern,Linear Scale

Channels 1, 2, & 3

Δ = 0.09 dB

Δ = 0.7 ns

Worst Case


Far Field Behavior vs Azimuth, Magnitude, Polar

RIGHT HAND CIRCULAR Polarization(co-pol)


Channels 1, 2, & 3

E_RH1

E_RH2

E_RH3

cv

0 45 90 135 180 225 270 315 3600

0.5

1

ns


Channels 1, 2, & 3

E_RH4

E_RH5

E_RH6

cv

0 45 90 135 180 225 270 315 3600.02

0.04

0.06

0.08

0.1

dB

EfarRH3 i

EfarRH8 i

EfarRH13 i

i

0

30

6090

120

150

180

210

240270

300

330


Channels 1, 2, & 3


Load Impedance Presented to Transmitter

Transmitter "Current Source" Azimuth = 0 deg

E_dB

Freq_kHz200 100 0 100 200

58

60

62

Lfeed_ft 501.75

E_Phase

Freq_kHz200 100 0 100 200

0

50

100

_ns

Freq_kHz200 100 0 100 200

200

0

200

Santkfreq

arg Santkfreq

0

30

6090

120

150

180

210

240270

300

330

0.5

0.4

0.3

0.2

0.1

0

Input Impedance, Plane

≈ 500 ft Transmission Line

Γ Plane


Far Field Behavior, Single Channel

Transmitter "Current Source" Azimuth = 0 deg

E_dB

Freq_kHz200 100 0 100 200

58

60

62

Lfeed_ft 501.75

E_Phase

Freq_kHz200 100 0 100 200

0

50

100

_ns

Freq_kHz200 100 0 100 200

200

0

200

Santkfreq

arg Santkfreq

0

30

6090

120

150

180

210

240270

300

330

0.5

0.4

0.3

0.2

0.1

0

Input Impedance, Plane

Δ = 1.87 dB

Δ = 251 ns


Far Field Behavior vs Azimuth, 3 ChannelsRIGHT HAND CIRCULAR Polarization(co-pol)

Lfeed_ft 501.75


Channels 1, 2, & 3

E_RH1

E_RH2

E_RH3

cv

0 45 90 135 180 225 270 315 360200

220

240

260

ns


Channels 1, 2, & 3

E_RH4

E_RH5

E_RH6

cv

0 45 90 135 180 225 270 315 3601.6

1.7

1.8

1.9

dB

Δ = 1.87 dB

Δ = 251 ns

Worst Case


Antenna Input Impedance, Γ Plane

Santkfreq

arg Santkfreq

0

30

60

90

120

150

180

210

240

270

300

330

0.008

0.006

0.004

0.002

0Antenna Input Match, Plane

RLantkfreq

freqkfreq

30

35

40

45

50

55

60



Return Loss, Antenna Input

Santkfreq

arg Santkfreq

0

30

60

90

120

150

180

210

240

270

300

330

0.008

0.006

0.004

0.002

0Antenna Input Match, Plane

RLantkfreq

freqkfreq

30

35

40

45

50

55

60




Δ = 0.2 dB

Δ = 2.2 ns

Transmitter "50 Ohm Source"

E_dB

Freq_kHz200 100 0 100 200

55.4

55.6

55.8

E_Phase

Freq_kHz200 100 0 100 200

55

50

45

_ns

Freq_kHz200 100 0 100 200

2

0

2


Far Field Behavior Vs Azimuth, 3 Channels

Δ = 0.25 dB

Δ = 3.49 ns

Worst Case

Transmitter "50 Ohm Source" RIGHT HAND CIRCULAR Polarization(co-pol)

Peak-to-peak Delay Variation across 400 kHz Channel vs Azimuth

Channels 1, 2, & 3

E_RH1

E_RH2

E_RH3

cv

0 45 90 135 180 225 270 315 3600

2

4

ns


Channels 1, 2, & 3

E_RH4

E_RH5

E_RH6

cv

0 45 90 135 180 225 270 315 3600

0.1

0.2

0.3

dB

EfarRH3 i

EfarRH8 i

EfarRH13 i

i

0

30

6090

120

150

180

210

240270

300

330



Far Field Behavior vs Azimuth, Magnitude, Polar

Transmitter "50 Ohm Source" RIGHT HAND CIRCULAR Polarization(co-pol)


Channels 1, 2, & 3

E_RH1

E_RH2

E_RH3

cv

0 45 90 135 180 225 270 315 3600

2

4

ns


Channels 1, 2, & 3

E_RH4

E_RH5

E_RH6

cv

0 45 90 135 180 225 270 315 3600

0.1

0.2

0.3

dB

EfarRH3 i

EfarRH8 i

EfarRH13 i

i

0

30

6090

120

150

180

210

240270

300

330



Load Impedance Presented to Transmitter

Santkfreq

arg Santkfreq

0

30

60

90

120

150

180

210

240

270

300

330

0.008

0.006

0.004

0.002

0

Transmitter Load Impedance, Plane

Γ Plane




Δ = 0.31 dB

Δ = 11.3 ns

Transmitter "Current Source"

E_dB

Freq_kHz200 100 0 100 200

60.6

60.8

61

E_Phase

Freq_kHz200 100 0 100 200

150

100

50

0

_ns

Freq_kHz200 100 0 100 200

10

0

10


Far Field Behavior vs Azimuth, 3 Channels

Δ = 0.31 dB

Δ = 11.3 ns

Worst Case

Transmitter "Current Source" RIGHT HAND CIRCULAR Polarization(co-pol)


Channels 1, 2, & 3

E_RH1

E_RH2

E_RH3

cv

0 45 90 135 180 225 270 315 3600

5

10

15

ns


Channels 1, 2, & 3

E_RH4

E_RH5

E_RH6

cv

0 45 90 135 180 225 270 315 3600

0.2

0.4

dB


Single Dipole, 98 MHz ± 200 kHz

• 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.

50 0.04 dB 0.01 ns 16.3 dB 1.44 dB 81 ns 16.3 dB 0.54 dB 32 ns 26.4 dB 0.30 dB 19 ns 32.0 dB

Source Z Δ Gain Δ Delay Antenna Return Loss


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


Summary of Results

• 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.

Source Transmission Variation, Variation,System Return Loss Impedance Line Length (nom) Amplitude(dB) Delay (ns)Array 1 18 dB 50 500' 0.09 0.7Array 1 18 dB 500 500' 1.87 251Array 2 40+ dB 50 500' 0.25 3.49Array 2 40+ dB 500 500' 0.31 11.3

Single Dipole 16 dB 50 200' 0.04 0.01Single Dipole 16 dB inf. 200' 1.44 81

Resistor 14 dB inf. 680' 3.52 600

computed envelope linearity of several fm broadcast antenna arrays j. dane jubera 2008 nab...

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