COMPUTED ENVELOPE LINEARITY OF SEVERAL FM BROADCAST ANTENNA ARRAYS J. Dane Jubera 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 MININEC TM for Antenna Z and Radiation Characteristics all balanced-mode mutual impedances are considered Mathcad TM for offline data reduction and network analysis

2008 NAB Engineering Conference 3 General System Configuration

2008 NAB Engineering Conference 4 “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, Z s = 50 Ω Norton Equivalent Current Source, Z s = 500 Ω Norton Equivalent Current Source, Z s = ∞ Ω Linear System Analysis

2008 NAB Engineering Conference 5 iBiquity Digital Corporation HD Radio TM 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 (F c – 200 kHz) to (F c +200 kHz), where F c 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 (F c ) shall be within 600 ns peak to peak from (F c – 200 kHz) to (F c +200 kHz).” [1] [1] Doc. No. SY_SSS_1026s, Rev D, February 18, 2005, “HD Radio FM Transmission System Specifications”

2008 NAB Engineering Conference 6 Top View of Panel System Reflector Panel Dipole Feed Region

2008 NAB Engineering Conference 7 Isometric View of Panel System

2008 NAB Engineering Conference 8 Top View of Offset Panel System

2008 NAB Engineering Conference 9 Flow Chart for MININEC TM 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.

2008 NAB Engineering Conference 10 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.

2008 NAB Engineering Conference 11 Results, Configuration 1 Source Impedance: 50 Ω

2008 NAB Engineering Conference 12 Antenna Input Impedance, Γ Plane

2008 NAB Engineering Conference 13 ≈ 18 dB over 3.5 MHz Return Loss, Antenna Input

2008 NAB Engineering Conference 14 Far Field Behavior, Single Channel Δ = 0.05 dB Δ = 0.3 ns

2008 NAB Engineering Conference 15 Far Field Behavior vs Azimuth, 3 Channels Δ = 0.09 dB Δ = 0.7 ns Worst Case

2008 NAB Engineering Conference 16 Far Field Behavior vs Azimuth, Magnitude, Polar

2008 NAB Engineering Conference 17 Results, Configuration 1 Source Impedance: 500 Ω

2008 NAB Engineering Conference 18 Load Impedance Presented to Transmitter ≈ 500 ft Transmission Line Γ Plane

2008 NAB Engineering Conference 19 Far Field Behavior, Single Channel Δ = 1.87 dB Δ = 251 ns

2008 NAB Engineering Conference 20 Far Field Behavior vs Azimuth, 3 Channels Δ = 1.87 dB Δ = 251 ns Worst Case

2008 NAB Engineering Conference 21 Results, Configuration 2 Source Impedance: 50 Ω

2008 NAB Engineering Conference 22 Antenna Input Impedance, Γ Plane

2008 NAB Engineering Conference 23 Return Loss, Antenna Input

2008 NAB Engineering Conference 24 Far Field Behavior, Single Channel Δ = 0.2 dB Δ = 2.2 ns

2008 NAB Engineering Conference 25 Far Field Behavior Vs Azimuth, 3 Channels Δ = 0.25 dB Δ = 3.49 ns Worst Case

2008 NAB Engineering Conference 26 Far Field Behavior vs Azimuth, Magnitude, Polar

2008 NAB Engineering Conference 27 Results, Configuration 2 ≈ 500 ft Transmission Line Source Impedance: 500 Ω

2008 NAB Engineering Conference 28 Load Impedance Presented to Transmitter Γ Plane ≈ 500 ft Transmission Line

2008 NAB Engineering Conference 29 Far Field Behavior, Single Channel Δ = 0.31 dB Δ = 11.3 ns

2008 NAB Engineering Conference 30 Far Field Behavior vs Azimuth, 3 Channels Δ = 0.31 dB Δ = 11.3 ns Worst Case

2008 NAB Engineering Conference 31 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 dB0.01 ns16.3 dB  1.44 dB81 ns16.3 dB  0.54 dB32 ns26.4 dB  0.30 dB19 ns32.0 dB Source Z Δ Gain Δ Delay Antenna Return Loss

2008 NAB Engineering Conference 32 Resistive Load, Non-Radiating Resistive Load (R L + j 0) Long Transmission Line, Lossless Current Source (Z s =  ) Evaluate voltage on load resistor vs frequency ρ=|Γ|, Γ = (R L -Z0)/(R L +Z0) For sufficiently long transmission line (≈ FM) Δt = 4ρ(L/v)/(1- ρ 2 ) 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

2008 NAB Engineering Conference 33 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.