# UHF-MOD AM/FM Modulation

The AM/FM modulation option allows to generate phase-coherent linear combinations of up to 3 oscillator frequencies. The direct measurement of (higher-order) sidebands in a variety of different modulation schemes, including amplitude modulation (AM) and frequency modulation (FM), can be conveniently set up. Unlike conventional double demodulation schemes, e.g. tandem demodulation, the user will not need multiple instruments and is also not limited in modulation frequencies by the maximum available demodulation bandwidth.

## UHF-MOD Key Features

• Two independent AM/FM modulation units with 3 frequency components each
• Amplitude modulation and demodulation (simultaneous)
• Frequency modulation and demodulation (simultaneous),
• Adjustable filter settings for each frequency component
• Dual-modulator (signal output) configuration
• Harmonic sideband analysis (2 sidebands)
• Sideband separation (single-sided modulation)

## UHF-MOD Functional Diagram

### UHF-MOD Amplitude Modulation

$s(t)=[A_c + A_m * \sin(\omega_m t) ] * \sin(\omega_c t)$

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 recovering an AM signal with a lock-in amplifier is to take advantage of its steep filters and time integration to extract the signals of interest. As the AM spectrum consists of 3 frequency components, the UHF-MOD uses 3 demodulators to demodulate all 3 frequencies simultaneously providing a 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 UHF Instrument. The generation of AM signals is useful for stimulus generation in the application, but can also be utilized for system testing purposes.

### UHF-MOD Frequency Modulation

$s(t)=\sin[\omega_ct +\frac{\omega_p}{\omega_m} *\sin(\omega_mt) ]$

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 UHF Instrument is capable to demodulate a signal of interest at several frequencies simultaneously, and the UHF-MOD option provides the FM demodulation at the carrier frequency and a selectable pair of sidebands (ωc ± n * ωm). For narrow-band operation, the peak frequency deviation and the modulation frequency shall satisfy the relation ωpm << 1, but the UHF-MOD option operates also above this limit with a decreasing accuracy, i.e. ωpm < 2.

### UHF-MOD User Benefits

• Single-box solution for bimodal, multi-modal measurement challenges, no intermediate signal conversion
• Easy to set up
• Simultanously obtain X, Y, R and Θ for up to 3 phase coherent frequency components (not possible with tandem demodulation)
• Modulation frequencies are not limited by the maximum demodulation bandwidth (tandem demodulation)
• Compatibility with UHF-PID option and External Reference allows that carrier and modulation frequency can be derived from a high-performance PLL and/or external source
• Ability to dicriminate signals from upper and lower sidebands
• Results can be added and subtracted with Arithmetic Unit

## UHF-MOD Specifications

 AM and FM Specifications ωc, fc: carrier frequency range 6 µHz - 600 MHz ωm, fm: modulation frequency range 6 µHz - 600 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