HF2LI-MOD AM/FM Modulation

The HF2LI-MOD is an option for the HF2LI and allows for the direct analysis of sidebands in dynamic AM (amplitude modulation) and FM (frequency modulation) schemes. This option helps the user to precisely measure periodic variations in the frequency or the amplitude of the application signal. Such schemes are typically applied in oscillator and resonator related setups.

HF2LI-MOD Key Features

  • Simultaneous amplitude modulation and demodulation
  • Simultaneous frequency modulation and demodulation
  • Dual-demodulator (input) and dual-modulator (output) configurations
  • Support for bimodal and multi-modal modulation for AFM
  • Harmonic analysis
  • Sideband separation (single-sided modulation)

HF2LI-MOD Upgrade and Compatibility

  • Requires HF2LI-MF Multi-Frequency option
  • Field-upgradeable option
  • Compatible with all other HF2LI options 

HF2LI-MOD Applications

  • Atomic Force Microscopy (AFM)
  • Kelvin Probe Force Microscopy (KPFM)
  • MEMS/NEMS Sensors, e.g. gyroscopes, accelerometers, high-Q resonators, etc.
  • Laser Spectroscopy

HF2LI-MOD Functional Diagram

HF2LI-MOD amplitude modulation

s(t) = [ Ac + Am * sin(ωmt) ] * sin(ωct)

In AM, the amplitude of a carrier signal changes periodically. In most applications, this modulation is small and therefore subject to noise. Recovering an AM signal with a lock-in amplifier relies on its steep filters and time integration to extract the signal of interest. As the AM spectrum consists of 3 frequency components, the MF-MOD option uses 3 demodulators to demodulate all 3 frequencies simultaneously and provide best-in-class signal recovery performance. Simultaneous amplitude modulation and demodulation can be entirely controlled from the LabOne user interface of the instrument.

HF2LI-MOD frequency modulation

s(t) = sin[ ωct + ωpm * sin(ωmt) ]

IIn FM, the frequency of a carrier signal varies periodically. As the modulation often constitutes a small signal and is therefore prone to noise, the demodulation provided by a lock-in amplifier can be advantageous thanks to its configurable filtering. The instrument demodulates the signal of interest at several frequencies simultaneously, and the MF-MOD option adds FM demodulation at the carrier frequency and at the first sidebands (ωc ± ωm). The frequency modulation operated by the HF2LI-MOD option is optimized for narrow-band operation: the peak frequency deviation ωp and the modulation frequency ωm must satisfy the relation ωpm << 1. Nevertheless, the HF2LI-MOD option also works at peak frequency deviations up to the limit ωpm < 2 with decreasing accuracy.

HF2LI-MOD user benefits

  • Single-box solution for bimodal and multi-modal measurements
  • Tandem demodulation with 1 lock-in amplifier (instead of 2)
  • Access to the phase of the modulating signal (not possible with tandem demodulation)
  • Compatibility with the HF2LI-PLL option to derive carrier and modulation frequency from a high-performance PLL
  • System asymmetries accounted for with single-sided demodulation 
  • Straightforward setup without tandem demodulation or intermediate signal conversions

HF2LI-MOD Specifications

Amplitude and frequency modulation
ωc, fc: carrier frequency range 0.7 µHz - 50 MHz
ωm, fm: modulation frequency range 0.7 µHz - 50 MHz
ωs, fs: sideband frequency fs = m * fc ± n * fm
Ac: amplitude of carrier signal Ac < Vrange
m,n: harmonic analysis m,n = 1 to 32
Amplitude modulation
hAM: AM modulation index hAM = Am / Ac
Am: amplitude of modulation signal Ac + Am < Vrange
Frequency modulation
hFM: FM modulation index hFM = fp / fm
ωp, fp: peak frequency deviation demodulation fp < 2 * fm
ωp, fp: peak frequency deviation modulation fp < 12'000 * fm

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