![]() The output signal of the signal generator is finally passed on to a control amplifier. Simplified diagram of a signal generator showing both frequency‑dependent methods to generate a sine wave. Figure 3 shows a very simplified diagram of a signal generator with both methods.įigure 3. A digital-to-analog converter (DAC) is used for low‑frequency signals. A direct digital synthesizer (DDS) sine wave generator is used to generate high‑frequency signals. Gamry Instruments uses two different methods to generate a waveform depending on the frequency range. For example, a single sine wave of a 10 µHz signal lasts over 27 hours. Low frequencies do not have an instrumental but more a practical limitation. In contrast to high frequencies, low‑frequency signals can be controlled more easily because they resemble slow processes. Instrumental artifacts such as stray capacitance and inductive effects can drastically limit the frequency range.įor more information on instrument limitations, performance, and accuracy, see Gamry’s application note at Accuracy Contour Plots – Measurement and Discussion Cell cables can have a huge influence on the quality and bandwidth of a signal. Other factors that determine the usable frequency range derive from the measurement setup. In order to handle those signals, the bandwidth of the control amplifier (CA) needs to be sufficiently high so that signals can be properly adjusted and applied to a cell. High‑frequency signals mean also fast signal changes (step height) which need to be processed by the control amplifier. However, not only the clock frequency restricts the usable frequency range. Hence f CLK is typically much higher than the maximum target frequency. In the second case (f = f Nyquist), the generated signal is only a triangle wave. You can also notice that the sine wave is much better represented the larger f CLK is compared to the signal frequency f, as more points can be used to create the signal. A sine wave signal can be first reproduced if the signal frequency is equivalent to (middle) or lower than f Nyquist (bottom). The generated signal is just a constant signal. You can see in Figure 2 that the sine wave cannot be reproduced if the signal frequency f is higher than f Nyquist (top). Influence of clock frequency on waveform generation. The black dots show the clock frequency of the signal generator and the green curve the actual signal.įigure 2. The red curve resembles the target sine wave signal. The limiting frequency is also known as Nyquist frequency f Nyquist (see Eq. 2).įigure 2 illustrates this in more detail. As a general rule, the clock frequency f CLK must be at least twice as big as the signal frequency. The clock frequency does not only define the step width of the generated signal but determines also the maximum achievable signal frequency. ![]() The sample rate (also called “clock rate” or “clockfrequency”) plays an important role. High‑frequency signals are generally the limiting factor in potentiostat instrumentation. Graphical representation of a sine wave showing its digitized staircase form in greater detail. The smaller these steps are the better a signal can be reproduced.įigure 1. The width (time scale) and height (amplitude scale) of each single step depend on the sample rate and the magnitude resolution. This means that a signal generator approximates the signal curve with a staircase form (see Figure 1). In the past, waveform signals were generated with analog methods older instruments used, for example, phase‑locked loops (PLL) to create a sine wave. f.īecause a detailed description of EIS goes beyond the scope of this technical note, we mainly focus on how sine wave signals are generated.įor more information on the theory of electrochemical impedance spectroscopy, see Gamry’s application note at Basics of Electrochemical Impedance Spectroscopy.The radial frequency can be also written as frequency f with ω = 2π ![]() With E t as the applied signal at time t, amplitude E 0, and the radial frequency ω. The general function of a sine wave has the form When performing EIS experiments, a sine wave signal with varying frequencies (potentiostatic or galvanostatic) is applied to a cell. But what exactly does this term describe and how meaningful is this parameter? Introduction Further, the term “frequency resolution” is discussed which is often mentioned in specification sheets for potentiostats. This Technical Note outlines how waveform signals are generated with a potentiostat. Waveform Generation and Frequency Resolution Purpose of This Note
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