The output is given by the equation:
e = E_{c} (1+m_{a}E_{m} sin(ω_{m}t))sin(ω_{c}t)
where
E_{c} is the carrier amplitude (unmodulated)
E_{m} is the modulation amplitude )
m_{a} is the depth of modulation (≡ modulation index)
ω_{m} is 2π x modulating frequency
ω _{c} is 2π x carrier frequency
Slant range of DME is dependent on aircraft height, transponder location and its associated environment, and geographical topography. Maximum range in ARINC 568 is quoted as up to 300 nmi up to an altitude of 75000 ft. The delay range quoted will allow for a transponder transmission range of approximately 400 nmi and its lower value is 0 nmi,(the default 50 µs usually allowed from receipt of an interrogator signal to the transponder response within the transponder itself). These values must not be exceeded.
This model has limited functionality. It does not provide for the variation of some of the parameters (such as the pulse timing and level). The model may be modified by the user to include such parameters in the interface properties.
e = E_{c} sin (ω_{c}t + m_{f} sin (ω_{m}t) )
m_{f} = k_{f} (E_{m} /ω_{m} )
where:
E_{c} = carrier amplitude (unmodulated)
E_{m} = modulation amplitude
ω_{c} = 2πx carrier frequency
m_{f} = deviation ratio (≡ modulation index)
ω_{m} = 2π x modulating frequency
k_{f} = frequency deviation
e = E_{c} sin (ω_{c}t + k_{p}E_{m} sin (ω_{m}t) )
where:
E_{c} = carrier amplitude (unmodulated)
E_{m} = modulation amplitude
ω_{c} = 2πx carrier frequency
ω_{m} = 2π x modulating frequency
k_{p} = phase deviation
For this signal, the allowable types are Voltage, Current and Power. All types must be consistent, thus for example, if the ac signal amplitude is specified in volts then the dc offset amplitude must also be specified in volts.
For this signal, the allowable types are Voltage, Current and Power.
For this signal, the allowable types are Voltage, Current and Power. All types must be consistent. Thus for example, if the ramp signal amplitude is specified in volts then the dc offset must also be specified in volts.
For this signal, the allowable types are Voltage and Power.
The outputs of the resolver secondaries are given by the following two equations:
Sine output
e_{s1} = KE_{r} sinθ sin(2πf_{r}t+φ)
Cosine output
e_{s2} = KE_{r} cosθ sin(2πf_{r}t+φ)
or
e_{s2} = KE_{r} sin(θ+π/2)sin(2πf_{r}t+φ)
where
K is the transformer ratio (trans_ratio), assuming K to be the same for both secondaries
E _{r} is the reference amplitude in the primary (ampl)
q is angular displacement of the rotor (angle)
f_{r} is the reference frequency of the signal in the primary (freq)
j is the zero index position of the rotor (zero_index)
Thus the operation of the resolver may be modeled as the product of two signals for each output.
Sine output
e_{s1} = (E_{r} sin(2πf_{r}t+φ)) x (Ksinθ)
Cosine output
e_{s2} = (E_{r} sin(2πf_{r}t+φ)) x (Ksin(θ+π/2))
For this signal, the allowable types are Voltage, Current and Power. All types must be consistent. Thus, for example, if the square wave amplitude is specified in volts then the DC Offset must also be specified in volts.
SSR_pulses = (0 us ,0.8 us, 1),
({0.000002+sls_dev}, 0.8 us, {sls_level}),
({p3_start}, 0.8 us, {p3_level})
where
sls_dev is the SLS Deviation from the interface properties
sls_level is the SLS Level from the interface properties
p3_start is the P3 Start Time as determined by the value of Interrogation Mode from the table below.
p3_level is the P3 Level from the interface properties
Interrogation mode (mode) |
P3 Start Time (p3_start) |
1 |
3µs |
2 |
5µs |
3 |
8µs |
A |
8µs |
B |
17µs |
C |
21µs |
D |
25µs |
For this signal, the allowable types are Voltage, Current and Power.
The response is initiated 3 us after the third pulse of a valid interrogation is received.
The parameters of the array of pulses are defined in the table. Pulses F1 and F2 must be present. Pulse X is not currently used and should be omitted, other pulses may be specified as required.
Pulse |
Start_Time |
Pulse_Width |
Level_Factor |
F1 |
0 |
0.45ms |
1 |
C1 |
1.45 ms |
0.45ms |
1 |
A1 |
2.9 ms |
0.45ms |
1 |
C2 |
4.35 ms |
0.45ms |
1 |
A2 |
5.8 ms |
0.45ms |
1 |
C4 |
7.25 ms |
0.45ms |
1 |
A4 |
8.7 ms |
0.45ms |
1 |
X |
10.15 ms |
0.45ms |
1 |
B1 |
11.6 ms |
0.45ms |
1 |
D1 |
13.05 ms |
0.45ms |
1 |
B2 |
14.5 ms |
0.45ms |
1 |
D2 |
15.95 ms |
0.45ms |
1 |
B4 |
17.4 ms |
0.45ms |
1 |
D4 |
18.85 ms |
0.45ms |
1 |
F2 |
20.3 ms |
0.45ms |
1 |
P1 |
24.65ms |
0.45ms |
1 |
e = (E_{m}E_{c} /2)cos(ω_{c} +ω_{m} )t+(E_{m}E_{c} /2)cos(ω_{c} -ω_{m} )t
where
E_{m} is the modulation signal amplitude
E _{c} is the carrier amplitude (unmodulated)
ω_{m} is 2π x modulating frequency
ω_{c} is 2π x carrier frequency
The outputs of the synchro stator windings are given by the following equations:
S1
E_{s1} = KE_{r} sin(θ-2Π/3)sin(2πf_{r}t+φ)
S2
E_{s2} = KE_{r} sinθ sin(2πf_{r}t+φ)
S3
E_{s2} = KE_{r} sin(θ+2π/3)sin(2πf_{r}t+φ)
K is the transformer ratio (trans_ratio), assuming K to be the same for all stator windings
E_{r} is the reference amplitude in the primary (ampl)
q is angular displacement of the rotor (angle)
f_{r} is the reference frequency of the signal in the primary (freq)
j is the zero index position of the rotor ( zero_index)
Thus the operation of the synchro may be modeled as the product of two signals for each output.
S1
E_{s1} = (E_{r} sin(2πf_{r}t+φ)) x (Ksin(θ-2π/3)
S2
E_{s2} = (E_{r} sin(2πf_{r}t+φ)) x (Ksin(θ))
S3
E_{s3} = (E_{r} sin(2πf_{r}t+φ)) x (Ksin(θ+2π/3))