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

  • Amplitude modulation and demodulation (simultaneous)
  • Frequency modulation and demodulation (simultaneous)
  • Dual-demodulator (input) and dual-modulator (output) configuration
  • Support for bimodal / multi-modal modulation for AFM
  • Harmonic analysis
  • Sideband separation (single-sided modulation)
  • Option upgradeable in the field

HF2LI-MOD Upgrade and Compatibility

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 is periodically changing (modulated). In most applications this modulation is small and is therefore subject to noise. The purpose of measuring an AM signal with a lock-in amplifier is to take advantage of its steep filters to recover the signal of interest. As the AM spectrum consists of 3 bands, the HF2LI-MOD uses 3 demodulators to demodulate all 3 band simultaneously providing the best-in-class signal recovery performance. Simultaneous amplitude modulation and demodulation is supported and can be entirely controlled from the graphical user interface of the HF2LI. The generation of AM signals is useful for stimulus generation in the application, but is also handy for system testing purposes.

HF2LI-MOD Frequency Modulation

s(t) = sin[ ωct + ωpm * sin(ωmt) ]

In FM the frequency of a carrier signal is periodically changing (modulated). As the modulation is often a small signal and therefore subject to noise, the demodulation with a lock-in amplifier can be advantageous thanks to its configurable filtering. The HF2LI Lock-in Amplifier is capable of demodulating a signal of interest at several frequencies simultaneously, and the HF2LI-MOD option provides the FM demodulation at the carrier frequency and at the first sidebands (ωc ± ωm). The HF2LI-MOD frequency modulation is optimized for narrow-band operation, meaning that the peak frequency deviation ωp and the modulation frequency ωm shall satisfy  ωpm << 1. However, the HF2LI-MOD operates also at peak frequency deviations up to the limit ωpm < 2 with a decreasing accuracy.

HF2LI-MOD User Benefits

  • Single-box solution for bimodal and multi-modal measurements
  • Tandem demodulation implemented using 1 lock-in amplifier (instead of 2)
  • Enables measurement of the phase of the modulating signal (not possible with tandem demodulation)
  • Compatibility with HF2LI-PLL option means that carrier and modulation frequency can be derived from a high-performance PLL
  • Accounting for system asymmetries with single-sided demodulation 
  • Easy to use: no tandem demodulation, no intermediate signal conversions

HF2LI-MOD Specifications

AM and FM Specifications
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
AM Specifications
hAM: AM modulation index hAM = Am / Ac
Am: amplitude of modulation signal Ac + Am < Vrange
FM Specifications
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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