In almost every electronic circuit, filters are used for a wide variety of frequency ranges, from a few hertz to the higher HF range. A filter allows signals from one range to pass and blocks another range. Low-pass, high-pass, and bandpass filters as well as bandstop filters can be generated either analogously or digitally, and filters can also be generated for higher frequencies using microstrip lines, waveguides, or coaxial cables.

Because a low-noise frequency response is particularly desirable in the audio range, the higher frequencies are filtered out accordingly, thus reducing the noise. Another important example is filtering before analog-to-digital conversion. In HF transmission, the baseband signal is modulated onto a carrier using a mixer before transmission. In addition to unwanted mixing results, this results in frequency images that have to be filtered out before the signal is amplified and transmitted.

In telephony, for example, the analog frequency range from 300 Hz to 3,400 Hz (speech) is transmitted, sampled at 8 kHz, and digitized, so the audio signal that carries our speech is filtered by the phone with a bandpass filter. A side effect is that not all voice frequencies get through, and the voice on the phone sounds “filtered.” Another example is the splitter used in DSL technology. Here, the frequency range for analog or digital telephony (signaling and voice) on the one hand and for digital data for internet use (DSL) on the other is divided. These can then be filtered out and used with the respective filter.

To effectively tune components such as filters, especially during the design phase, the use of measurement technology is necessary. Spectrum analyzers (e.g., the RIGOL DSA800 series) or vector network analyzers (VNAs, e.g., the RIGOL RSA3000N series) can be used for high-frequency applications. However, conventional spectrum analyzers are not suitable for the low-frequency range, as they usually have a starting frequency range of 9 kHz and the required tracking generator only starts at 100 kHz. On the other hand, it is not possible to measure the phase over the frequency range with analyzers using the heterodyne principle.

While the second problem can be solved with a VNA, the first problem remains unsolved. One of the most helpful tools for displaying the transmission characteristics of a component, however, is the Bode diagram.

The Bode diagram is a full logarithmic plot for gain and a semi-logarithmic plot for phase. This means that for gain, both the Y-axis for the amplitude difference and the X-axis for the frequency are displayed logarithmically. Even the smallest changes over a very large frequency range can be displayed here. In the phase display, the X-axis is shown in degrees (°).

With this, not only filters but also operational amplifier circuits or control circuits can be measured.

With the MSO5000 series oscilloscope and the Bode plot function, RIGOL offers an optimal solution for carrying out these tests precisely for the lower frequency range from 10 Hz to 25 MHz. For this, you can use one of the two AWG generator outputs (25 MHz/200 MSa/s/14 bit) on the MSO5000. These generators also offer output of arbitrary signals up to 16 kpts in length, as well as many built-in basic waveforms and analog modulation types. With the arbitrary function, measured signals that can be seen on the display can be loaded into the generator and stored in the device in order to constantly output them for further analysis.

The Bode plotter is a highly useful tool to plot the frequency response of a circuit (such as that of a filter). On the one hand, these curves can be represented as locus curves that contain the magnitude and phase information. Additionally, however, the visualization over the frequency range serves to enable a better understanding. The change in the voltage amplitude as well as the phase behavior can be displayed and measured in two separate curves. The MSO5000 series outputs harmonic AC signal frequencies from one of the two AWG outputs. The vertical representation of the amplitude variation (i.e., the positive or negative amplification of the transformer) is specified in decibels (Formula 1):

The phase change is specified (non-logarithmically) in degrees. The output of the generator can be separated with a power splitter and is connected to analog input 1 of the oscilloscope on the one hand and to the measurement object (e.g., a filter) on the other. The output of the filter is connected to analog input 2. With channel 1, channel 2, and the sine sweep over the frequency range of the MSO5000 generator, the transfer function can now be displayed. The structure of the measurement is shown in Figure 1.

To describe the functions of the Bode plot in the MSO5000 Series oscilloscope, a simple filter is used as an example. A low-pass filter (Figure 2) lets pass all frequency components from a low frequency range — e.g., 0 Hz up to the upper limit frequency — and blocks all higher-frequency components.

Figure 2 characterizes the frequency response of the amplitude and the phase curve over the frequency range of the filter. In this example, the cutoff frequency is defined by the 3-dB reduction or by the phase position of the filter at –45°. When designing the filter, both values can be achieved by precisely setting the passive components such as resistors, inductances, or capacitances. For example, simple RC elements can be used up to approximately 100 kHz. Higher frequency ranges are implemented with RLC elements, among other things.

Mathematically, they can be described as in Formula 2 for a simple first-order RC low-pass filter:

Formula 2 shows that the cut-off frequency of the filter can be defined by selecting the resistance (R) and the capacitance (C). The amount and the angle can be calculated from Formula 3, which then also corresponds to the curve in Figure 1:

Different parameters can be measured in the Bode diagram. The phase margin (PM) describes the phase distance from 0° to the real measurement point at the position where the gain is 0 dB. The higher the value, the higher the stability. Similar to PM, the amplifier margin (GM) is a measure of relative stability.

Here, with a phase position of 0°, the amplitude difference is measured at 0 dB and automatically marked in the Bode diagram. The higher this value, the better the stability. Both values are shown in Figure 3 using an example measurement.

In some circuits that use amplifiers, for example, amplitudes that are too low can produce an incorrect result because the output amplitude is too small to produce a gain value that can be evaluated. To remedy the problem, the MSO5000 offers amplitude variation over the frequency range. This means that a higher input amplitude could be set in the lower decades and a lower amplitude value for the higher frequencies.

When measuring the input and output voltage, it is important to use the right probe. The standard accessory probes of the PVP2350 version can be operated with two different gains. The filter measurement in Figure 4 shows the phase curve and the frequency response of the amplitude change.

The effects of a filter can also be illustrated with the integrated FFT in a frequency measurement. In Figure 5, a sine wave signal was fed into the filter from Figure 4 and measured at the filter output. The result is shown in the frequency domain of the MSO5000 Series oscilloscope.

RIGOL’s UltraVision II–capable oscilloscopes have a variety of standard or optional functions. The multiple possibilities of the oscilloscope offer an optimal solution for a variety of applications, especially in the field of research and development, in industry, or in education. The MSO5000 series are powerful measuring devices that offer uncompromising quality and performance at an unprecedented price. In addition to the standard probes already included, the devices also offer a wide range of current clamps, high-voltage and differential probes, and much more as an option.

Boris Adlung is sales manager at RIGOL Technologies EU GmbH