Models 1455A & 1451A Frequency Response Analyzers
for use with Model 1470E

The Model 1455A and 1451A frequency response analyzers use state-of-the-art digital signal processor (DSP) technology together with a wide range of impedance analysis techniques (including single sine correlation, harmonic analysis and multi-sine / FFT) to provide the ultimate in impedance measurement performance when used with the Model 1470E eight channel potentiostat/galvanostat.

Each FRA consists of a module that is plugged into a Model 1400A chassis, which accommodates up to eight modules. Interconnecting cables are used to connect the FRA generator outputs and analyzer inputs to the corresponding channels on the Model 1470E, while each module's dedicated Ethernet connection allows full control from the associated computer.

The two models of FRA differ only in their upper frequency limit, which is 1 MHz in the case of the 1455A, and 100 kHz in the case of the 1451A. The lower operating frequency in both cases is 10 µHz.

Both models support classic single sine as well as the potentially faster multisine correlation modes.

Single sine correlation
Single sine correlation is recognized by impedance researchers throughout the world, as being the most accurate and repeatable technique available for the investigation of cell impedance. The models 1455A and 1451A provide very high measurement rates, allowing detailed impedance scans from 1 MHz to 10 Hz to be performed in just a few seconds. The single sine correlation technique is available across the entire bandwidth of the system (from 10 μHz to 100 kHz/1 MHz).

Multi-sine / FFT analysis
At high frequency, the single sine correlation technique provides very fast impedance analysis. At lower frequency however, for example where cell diffusion characteristics need to be analyzed, the measurement time may become extended since at least one cycle of the waveform must be analyzed at each frequency. This may result in tests that run into several hours. For example, a single frequency measurement at 1 mHz takes 1000 seconds (>16 minutes).

The models 1455A and 1451A however, provide an alternative measurement technique (multi-sine / Fast Fourier Transform FFT analysis), which is available across the entire frequency range of the system but is particularly efficient for low frequency tests. In this mode, multiple sinewave frequencies are simultaneously applied to the cell, providing stimulus throughout the frequency range of interest. The multi-sine waveform looks similar to random noise but actually is a waveform containing only the selected frequencies. The voltage and current waveforms from the cell are simultaneously captured and analyzed using the FFT technique and the ratio of the spectral data provides impedance results at all of the frequencies in the original stimulus waveform.

For example, three frequency decades may be selected with a base frequency of 1 mHz providing simultaneous impedance results from 1 Hz to 1 mHz with 1 mHz resolution in a single measurement timeframe of 1000 seconds (16 minutes). By comparison, a single sine correlation analysis from 1 Hz to 1 mHz at 10 points per decade would take around 80 minutes (five times as long). This makes the multi-sine / FFT approach suited to applications where the speed of measurement is critical, for example, measurements of time variant cells where measurements need to be performed quickly before the cell changes.

The technique is fast but may be less accurate than single sine correlation due to issues related to simultaneous measurement of multiple frequencies. However, the units provide some very advanced facilities to help the user to minimize these effects by providing:

• user selection of frequencies that are present in the applied multi-sine waveform 
• a default frequency list as an aid to appropriate frequency selection 
• automatic waveform optimization to minimize any peaks on the multi-sine waveform

The frequency selection facility allows measurement noise to be reduced by using fewer frequencies in the multi-sine waveform since each frequency will then be of greater amplitude while maintaining the same overall stimulus level. The frequency selection facility can also be used to minimize issues caused by electrochemical cell non-linearity and to obtain virtually logarithmically spaced data; giving very similar results to the swept sine correlation technique while retaining the speed advantage of the FFT.

Specifications