Constants & Parameters

All constants are defined in apollo.constants and trace directly to the 1965 NAA Telecommunication Systems Study Guide (Course A-624) via the IMPLEMENTATION_SPEC.md section references noted in each table.

from apollo.constants import DOWNLINK_FREQ_HZ, PCM_HIGH_BIT_RATE, SCO_FREQUENCIES

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RF Carrier Frequencies

IMPL_SPEC section 2.1.

Constant	Value	Unit	Description
DOWNLINK_FREQ_HZ	2,287,500,000	Hz	Downlink carrier: spacecraft to ground (2287.5 MHz)
UPLINK_FREQ_HZ	2,106,406,250	Hz	Uplink carrier: ground to spacecraft (2106.40625 MHz)
COHERENT_RATIO	(240, 221)	—	Coherent turnaround ratio: Tx = Rx x 240/221
VCO_REFERENCE_HZ	19,062,500	Hz	Master oscillator reference (19.0625 MHz)

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Modulation Parameters

IMPL_SPEC section 2.3.

Constant	Value	Unit	Description
PM_PEAK_DEVIATION_RAD	0.133	rad	Peak phase deviation (7.6 degrees)
PM_SENSITIVITY_RAD_PER_V	0.033	rad/V	PM sensitivity at 1 kHz
FM_VCO_SENSITIVITY_HZ_PER_V	1,500,000	Hz/V	FM VCO sensitivity (1.5 MHz peak / V peak)
FM_MODULATION_BW_HZ	1,500,000	Hz	FM modulation bandwidth (5 Hz to 1.5 MHz)

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Subcarrier Frequencies

IMPL_SPEC section 4.2.

Downlink Subcarriers

Constant	Value	Unit	Description
PCM_SUBCARRIER_HZ	1,024,000	Hz	PCM telemetry subcarrier (1.024 MHz, BPSK modulated)
VOICE_SUBCARRIER_HZ	1,250,000	Hz	Voice subcarrier (1.25 MHz, FM modulated)
EMERGENCY_KEY_HZ	512,000	Hz	Emergency keyed carrier (512 kHz)

PCM Bandpass Filter

Constant	Value	Unit	Description
PCM_BPF_LOW_HZ	949,000	Hz	Lower edge of PCM bandpass filter
PCM_BPF_HIGH_HZ	1,099,000	Hz	Upper edge of PCM bandpass filter
PCM_BPF_BW_HZ	150,000	Hz	PCM bandpass filter bandwidth (derived: HIGH - LOW)

Voice Channel

Constant	Value	Unit	Description
VOICE_FM_DEVIATION_HZ	29,000	Hz	Voice FM deviation (+/-29 kHz)
VOICE_AUDIO_LOW_HZ	300	Hz	Voice audio passband lower edge
VOICE_AUDIO_HIGH_HZ	3,000	Hz	Voice audio passband upper edge

Uplink Subcarriers

IMPL_SPEC section 2.2.

Constant	Value	Unit	Description
UPLINK_VOICE_SUBCARRIER_HZ	30,000	Hz	Uplink voice subcarrier (30 kHz FM)
UPLINK_DATA_SUBCARRIER_HZ	70,000	Hz	Uplink data subcarrier (70 kHz FM)

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Master Clock & Timing

IMPL_SPEC section 5.5.

Constant	Value	Unit	Description
MASTER_CLOCK_HZ	512,000	Hz	CTE master clock (512 kHz). All timing derived from this

The master clock divides to produce both bit rates:

• High rate: 512 kHz / 10 = 51.2 kHz
• Low rate: 512 kHz / 320 = 1.6 kHz

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PCM Telemetry Parameters

IMPL_SPEC sections 5.1, 5.2.

High Bit Rate

Constant	Value	Unit	Description
PCM_HIGH_BIT_RATE	51,200	bps	High bit rate (51.2 kbps NRZ, MSB first)
PCM_HIGH_CLOCK_DIVIDER	10	—	Master clock divisor: 512 kHz / 10
PCM_HIGH_WORD_RATE	6,400	words/s	Word rate at high bit rate
PCM_HIGH_WORDS_PER_FRAME	128	words	Words per frame at high rate
PCM_HIGH_FRAMES_PER_SEC	50	fps	Frame rate at high bit rate
PCM_HIGH_FRAME_PERIOD_US	19,968	us	Frame period in microseconds

Low Bit Rate

Constant	Value	Unit	Description
PCM_LOW_BIT_RATE	1,600	bps	Low bit rate (1.6 kbps)
PCM_LOW_CLOCK_DIVIDER	320	—	Master clock divisor: 512 kHz / 320
PCM_LOW_WORD_RATE	200	words/s	Word rate at low bit rate
PCM_LOW_WORDS_PER_FRAME	200	words	Words per frame at low rate
PCM_LOW_FRAMES_PER_SEC	1	fps	Frame rate at low bit rate

Frame Structure

Constant	Value	Unit	Description
PCM_WORD_LENGTH	8	bits	Bits per telemetry word
PCM_SYNC_WORD_LENGTH	32	bits	Sync pattern length (4 words)
PCM_SYNC_A_LENGTH	5	bits	Selectable A field width
PCM_SYNC_CORE_LENGTH	15	bits	Fixed core pattern width (complemented on odd frames)
PCM_SYNC_B_LENGTH	6	bits	Selectable B field width
PCM_SYNC_FRAME_ID_LENGTH	6	bits	Frame ID field width (encodes 1-50)

Subframe Timing

Constant	Value	Unit	Description
SUBFRAME_FRAMES	50	frames	Frames per subframe (high rate)
SUBFRAME_PERIOD_S	1.0	s	Subframe period

Default Sync Word Fields

These are the patchboard-configurable values used as defaults. On real hardware, these were set by wiring jumpers on the PCM encoder.

Constant	Value (binary)	Value (decimal)	Description
DEFAULT_SYNC_A	10101	21	5-bit A field
DEFAULT_SYNC_CORE	111001101011100	29404	15-bit fixed core (even-frame value)
DEFAULT_SYNC_B	110100	52	6-bit B field

Note

The sync word bit layout is [5-bit A][15-bit core][6-bit B][6-bit frame_id] = 32 bits total. The 15-bit core is bitwise-complemented on odd-numbered frames. See the protocol reference for generation and parsing functions.

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A/D Converter (Coder)

IMPL_SPEC section 5.3.

Constant	Value	Unit	Description
ADC_BITS	8	bits	ADC resolution
ADC_ZERO_CODE	1	—	Code for 0V input (00000001)
ADC_FULLSCALE_CODE	254	—	Code for 4.98V input (11111110)
ADC_OVERFLOW_CODE	255	—	Code for >5V input (11111111)
ADC_FULLSCALE_VOLTAGE	4.98	V	Full-scale input voltage
ADC_STEP_MV	19.7	mV	Voltage per least-significant bit
ADC_LOW_LEVEL_GAIN	125	—	Gain multiplier for low-level inputs (0-40 mV range)

The conversion formula is:

voltage = (code - 1) * 4.98 / 253

For low-level inputs (0-40 mV), the amplifier applies x125 gain before digitization. To recover the actual input voltage, divide by 125.

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Subcarrier Oscillators (FM Mode)

IMPL_SPEC section 4.3. These 9 SCO channels are present only in FM downlink mode.

Constant	Value	Unit	Description
SCO_DEVIATION_PERCENT	7.5	%	Deviation as percentage of center frequency (+/-)
SCO_INPUT_RANGE_V	(0.0, 5.0)	V	DC input voltage range
SCO_OUTPUT_LEVEL_V	0.707	V	Peak output level into 5.11 kOhm

SCO Channel Frequencies

SCO_FREQUENCIES is a dict mapping channel number to center frequency:

SCO Channel	Center Frequency (Hz)	Deviation +/- (Hz)	Low Freq (Hz)	High Freq (Hz)
1	14,500	1,087.5	13,412.5	15,587.5
2	22,000	1,650.0	20,350.0	23,650.0
3	30,000	2,250.0	27,750.0	32,250.0
4	40,000	3,000.0	37,000.0	43,000.0
5	52,500	3,937.5	48,562.5	56,437.5
6	70,000	5,250.0	64,750.0	75,250.0
7	95,000	7,125.0	87,875.0	102,125.0
8	125,000	9,375.0	115,625.0	134,375.0
9	165,000	12,375.0	152,625.0	177,375.0

All SCOs map 0-5V DC input linearly to the frequency deviation range. 0V corresponds to the low frequency limit, 2.5V to the center, and 5V to the high frequency limit.

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Virtual AGC Interface

IMPL_SPEC section 1.

Connection

Constant	Value	Unit	Description
AGC_PORT_BASE	19697	—	TCP port base for yaAGC socket connections
AGC_MAX_CLIENTS	10	—	Maximum concurrent client connections

AGC I/O Channels

Channels are defined in octal in the original AGC documentation. The constants store decimal equivalents.

Constant	Octal	Decimal	Description
AGC_CH_INLINK	045	37	Uplink data input (ground to AGC)
AGC_CH_OUTLINK	057	47	Downlink data output (AGC to ground)
AGC_CH_DNTM1	034	28	Telemetry word 1 (high byte)
AGC_CH_DNTM2	035	29	Telemetry word 2 (low byte)
AGC_CH_OUT0	010	8	Relay rows
AGC_CH_DSALMOUT	011	9	DSKY alarms
AGC_CH_CHAN13	013	11	Radar activity
AGC_CH_CHAN30	030	24	Status/alarm bits
AGC_CH_CHAN33	033	27	AGC warning input

Telecom Channel Set

AGC_TELECOM_CHANNELS is a frozenset containing the four primary telecom channels used by the bridge filter:

AGC_TELECOM_CHANNELS = frozenset({
    AGC_CH_INLINK,    # 37  (045 octal)
    AGC_CH_OUTLINK,   # 47  (057 octal)
    AGC_CH_DNTM1,     # 28  (034 octal)
    AGC_CH_DNTM2,     # 29  (035 octal)
})

Downlink Buffer

Constant	Value	Unit	Description
AGC_DOWNLINK_BUFFER_WORDS	400	15-bit words	Size of one complete downlink data snapshot

Downlink List Type IDs

From DecodeDigitalDownlink.c in the Virtual AGC project:

Constant	Value	Description
DL_CM_POWERED_LIST	0	CM Powered Flight
DL_LM_ORBITAL_MANEUVERS	1	LM Orbital Maneuvers
DL_CM_COAST_ALIGN	2	CM Coast/Alignment
DL_LM_COAST_ALIGN	3	LM Coast/Alignment
DL_LM_DESCENT_ASCENT	7	LM Descent/Ascent
DL_LM_LUNAR_SURFACE_ALIGN	8	LM Lunar Surface Alignment
DL_CM_ENTRY_UPDATE	9	CM Entry Update

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Uplink Modulation Parameters

IMPL_SPEC section 2.2. These parameters define the uplink RF modulation characteristics — the signal path from ground station to spacecraft.

Constant	Value	Unit	Description
UPLINK_PM_DEVIATION_RAD	1.0	rad	Peak PM deviation (57.3 degrees — much stronger than downlink’s 0.133 rad)
UPLINK_DATA_BIT_RATE	2,000	bps	Uplink command data rate (2 kbps NRZ)
UPLINK_DATA_FM_DEVIATION_HZ	4,000	Hz	FM deviation on the 70 kHz data subcarrier (±4 kHz)
UPLINK_VOICE_FM_DEVIATION_HZ	7,500	Hz	FM deviation on the 30 kHz voice subcarrier (±7.5 kHz)
UPLINK_WORD_BITS	15	bits	AGC word width (matches AGC 15-bit architecture)
UPLINK_INTER_WORD_GAP	3	bit periods	Zero-bit gap between serialized words (UPRUPT timing margin)

Tip

The uplink PM deviation (1.0 rad) is nearly 8× the downlink deviation (0.133 rad). The ground station had a 26-meter dish and kilowatt-class transmitter — the asymmetry was intentional to overcome the spacecraft’s low-gain antenna during emergency modes.

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PRN Ranging

Ken Shirriff’s research and NASA documentation. The ranging system measures Earth-Moon distance by correlating a pseudo-random noise (PRN) code.

Chip Rate & Code Length

Constant	Value	Unit	Description
RANGING_CHIP_RATE_HZ	993,963	chip/s	PRN chip rate (~994 kchip/s)
RANGING_CODE_LENGTH	5,456,682	chips	Full code period: 2 × 11 × 31 × 63 × 127
SPEED_OF_LIGHT_M_S	299,792,458	m/s	Used for delay-to-range conversion

Component Code Lengths

The PRN code is built from five component codes combined with majority-vote logic:

Constant	Value	Description
RANGING_CL_LENGTH	2	Clock component (alternating 0/1)
RANGING_X_LENGTH	11	X code (custom feedback logic)
RANGING_A_LENGTH	31	A code (5-bit LFSR)
RANGING_B_LENGTH	63	B code (6-bit LFSR)
RANGING_C_LENGTH	127	C code (7-bit LFSR)

LFSR Generator Parameters

Initial states and feedback tap positions for each linear feedback shift register:

Constant	Value	Description
RANGING_X_INIT	22 (0b10110)	X code initial register state
RANGING_A_INIT	0x1F (all ones)	A code initial state (5-bit)
RANGING_B_INIT	0x3F (all ones)	B code initial state (6-bit)
RANGING_C_INIT	0x7F (all ones)	C code initial state (7-bit)
RANGING_A_TAPS	(2, 0)	A LFSR feedback: x⁵ + x² + 1
RANGING_B_TAPS	(1, 0)	B LFSR feedback: x⁶ + x + 1
RANGING_C_TAPS	(1, 0)	C LFSR feedback: x⁷ + x + 1

Note

The X code uses custom nonlinear feedback logic (not a standard LFSR), derived from Ken Shirriff’s analysis of the original Apollo hardware. The tap values above apply only to the A, B, and C codes. See RangingCodeGenerator.generate_x() for the X code implementation.

Range Resolution

At ~994 kchip/s, one chip ≈ 1.006 μs. For two-way ranging:

range_resolution ≈ c / (2 × chip_rate) ≈ 150.8 m per chip

The full code period covers approximately 5.49 seconds of round-trip delay, equivalent to ~822,600 km one-way range — more than enough for Earth-Moon distance (~384,400 km).

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Recommended Sample Rates

Constant	Value	Unit	Description
SAMPLE_RATE_BASEBAND	5,120,000	Hz	Baseband rate: 10x master clock (5.12 MHz)
SAMPLE_RATE_RF	10,240,000	Hz	RF rate: 20x master clock (10.24 MHz)

Both rates are integer multiples of the 512 kHz master clock, ensuring clean relationships with all PCM timing.

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Receiver PLL Parameters

IMPL_SPEC section 2.2.

Constant	Value	Unit	Description
RX_PLL_BW_HZ	318	Hz	PLL bandwidth at threshold
RX_STATIC_PHASE_ERROR_DEG	6.0	degrees	Maximum static phase error
RX_AGC_RANGE_DB	80	dB	AGC dynamic range (-132 to -52 dBm)
RX_AGC_TIME_CONSTANT_S	5.7	s	AGC time constant
RX_THRESHOLD_DBM	-132.5	dBm	Receiver sensitivity threshold

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Transmitter Parameters

IMPL_SPEC section 2.3 and 3.1.

Constant	Value	Unit	Description
TX_POWER_MW	300	mW	Transmitter power (250-400 mW typical)
TX_IMPEDANCE_OHM	50	Ohm	Output impedance

Traveling Wave Tube (TWT) Amplifier

Constant	Value	Unit	Description
TWT_LOW_POWER_W	5	W	TWT low power mode
TWT_HIGH_POWER_W	20	W	TWT high power mode
TWT_WARMUP_S	90	s	TWT warmup time