Harmonic Mixing

The Si5351 frequency synthesizer has a practical upper limit around 200-300 MHz. To measure at VHF, UHF, and beyond, the NanoVNA-H uses a clever technique: harmonic mixing. By generating a fundamental frequency and mixing with its odd harmonics, the VNA can measure up to 1.5 GHz or higher.

Frequency Coverage: 600 Hz – 2 GHz

Ultra-Low

Low

Direct

3rd Harmonic

5th Harmonic

7th Harmonic

1 kHz

100 kHz

1 MHz

10 MHz

100 MHz

290 MHz

1 GHz

2 GHz

Signal Generation Method

Direct (fundamental)

3rd harmonic

5th harmonic

7th harmonic

Dynamic Range

Direct: >70 dB

3rd Harmonic: ~50 dB

5th Harmonic: ~40 dB

7th Harmonic: ~30 dB

Harmonic threshold: ~290 MHz (SA612A) or ~300 MHz (ZeeTK NE602A)

The Frequency Threshold

The firmware defines a boundary where it switches from direct synthesis to harmonic mode:

// From nanovna.h
#ifdef __ZEETK__
#define FREQUENCY_THRESHOLD      300000110U   // 300 MHz for ZeeTK NE602A
#else
#define FREQUENCY_THRESHOLD      290000110U   // 290 MHz for SA612A
#endif

• Below threshold: Direct frequency synthesis
• Above threshold: Harmonic mixing with odd harmonics (3rd, 5th, 7th…)

Mixer Dependency

The exact threshold depends on the mixer chip. The original SA612A works best up to ~290 MHz, while the ZeeTK NE602A extends this slightly to ~300 MHz.

How Harmonic Mixing Works

Square Wave Harmonics

The Si5351 outputs square waves, which are rich in odd harmonics:

Square wave = sin(f) + (1/3)sin(3f) + (1/5)sin(5f) + (1/7)sin(7f) + ...

Harmonic	Relative Amplitude	dB below fundamental
1st (fundamental)	1.000	0 dB
3rd	0.333	-9.5 dB
5th	0.200	-14 dB
7th	0.143	-17 dB
9th	0.111	-19 dB

Mixing Process

To measure at frequency f_target:

1. Generate fundamental at f_fund = f_target / harmonic_number
2. The DUT sees the harmonic component at f_target
3. The LO also generates harmonics at f_target + IF_offset
4. Mixing produces the same IF frequency as direct mode

flowchart LR
  subgraph RF Path
      SI[Si5351<br/>100 MHz] --> |3rd harmonic| DUT[DUT<br/>300 MHz]
  end

  subgraph LO Path
      LO[Si5351<br/>100 MHz + IF/3] --> |3rd harmonic| MIX[Mixer]
  end

  DUT --> MIX
  MIX --> IF[IF Output<br/>12 kHz]

Harmonic Level Detection

The firmware determines which harmonic to use based on the target frequency:

uint32_t si5351_get_harmonic_lvl(uint32_t freq) {
  if (freq < FREQUENCY_THRESHOLD)
    return 1;  // Direct mode

  // Find lowest odd harmonic that puts fundamental in range
  uint32_t harmonic = 3;
  while (freq / harmonic > (FREQUENCY_THRESHOLD - 10000000))
    harmonic += 2;  // Only odd harmonics

  return harmonic;
}

Harmonic Selection Table

Target Frequency	Harmonic	Fundamental Frequency
50 - 290 MHz	1st (direct)	50 - 290 MHz
290 - 870 MHz	3rd	97 - 290 MHz
870 - 1450 MHz	5th	174 - 290 MHz
1450 - 2000 MHz	7th	207 - 286 MHz

Impact on Dynamic Range

Harmonic mixing reduces dynamic range because:

1. Lower harmonic power: 3rd harmonic is 9.5 dB down
2. Double the loss: Both RF and LO are reduced
3. Total penalty: Approximately 19 dB for 3rd harmonic

Dynamic Range (harmonic) = Dynamic Range (direct) - 20*log10(1/N)

Where N is the harmonic number.

Mode	Harmonic	Typical Dynamic Range
Direct	1st	> 70 dB
3rd harmonic	3rd	~ 50-55 dB
5th harmonic	5th	~ 40-45 dB
7th harmonic	7th	~ 35-40 dB

UHF Limitations

Above 1 GHz, dynamic range is significantly reduced. Measurements requiring high dynamic range (like filter stopband rejection) may be unreliable. Consider using an external directional coupler for critical UHF measurements.

Frequency Offset Adjustment

In harmonic mode, the IF offset must be divided by the harmonic number to maintain the correct final IF:

// When generating LO for harmonic mode
uint32_t lo_offset = FREQUENCY_OFFSET / harmonic;

// LO fundamental = target/harmonic + IF_offset/harmonic
// LO at harmonic = target + IF_offset (same as direct mode)

Calibration at Harmonic Boundaries

The transition between direct and harmonic modes creates a discontinuity in the error terms. The calibration interpolation routine handles this specially:

// From main.c cal_interpolate()
uint32_t hf0 = si5351_get_harmonic_lvl(src_f0);
if (hf0 != si5351_get_harmonic_lvl(src_f1)) {
  // Points span a harmonic boundary
  // Cannot interpolate across - must extrapolate within same mode
  if (hf0 == si5351_get_harmonic_lvl(f)) {
    // Use points from current harmonic region
    // ... extrapolation code
  }
}

Calibration Strategy

For measurements spanning the 290 MHz boundary, consider:

1. Separate calibrations for below and above 290 MHz
2. Extra calibration points near the boundary
3. Avoiding narrow spans that cross the boundary

Spurious Responses

Harmonic mixing can create spurious responses (spurs) from:

1. Unwanted harmonic combinations: RF 3rd mixing with LO 5th
2. Image frequencies: (LO - RF) as well as (LO + RF) products
3. Intermodulation: From non-linearities in mixers

Spur Frequencies

Common spur patterns near 290 MHz boundary:

Spur Type	Frequency	Mitigation
3rd-5th mixing	Various	Filtering
LO leakthrough	At LO freq	Isolation
Half-IF	At IF/2 offset	Careful cal

The firmware includes some spur mitigation:

// Avoid exact harmonic boundary
#define FREQUENCY_THRESHOLD      290000110U  // Not exactly 290 MHz

The odd offset (110 Hz) prevents the fundamental and harmonic frequencies from landing on exact multiples that might produce coherent spurs.

Practical Implications

What Works Well

• Antenna SWR at UHF: Return loss up to ~30 dB measurable
• Filter passbands: Good for tuning UHF filters
• Relative measurements: Comparing similar DUTs

What Is Challenging

• Filter stopband: May not see > 40 dB rejection
• High-isolation measurements: Limited by harmonic mode range
• Phase accuracy at UHF: Increased phase noise

Hardware Variations

Different mixer chips affect harmonic performance:

Chip	Frequency Coverage	Notes
SA612A (NXP)	Up to ~290 MHz direct	Original chip, discontinued
NE602A (ZeeTK)	Up to ~300 MHz direct	Drop-in replacement
Both	To 1.5+ GHz harmonics	With reduced dynamic range

#ifdef __ZEETK__
#define FREQUENCY_THRESHOLD      300000110U   // ZeeTK allows higher
#else
#define FREQUENCY_THRESHOLD      290000110U   // SA612A more conservative
#endif

Summary

Parameter	Direct Mode	3rd Harmonic	5th Harmonic
Frequency	0-290 MHz	290-870 MHz	870-1450 MHz
Dynamic Range	> 70 dB	~50 dB	~40 dB
Phase Noise	Lowest	Moderate	Higher
Calibration	Normal	Discontinuity	Discontinuity

Next Steps

Learn how the firmware manages real-time tasks in Threading Model.