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Oscilloscope helps obtain Bode plots in non-50Ω environments

A Bode plot can simplify characterization of an active or a passive network by showing frequency and phase representations of the network’s transfer function, T. In its classic form, a Bode plot graphs frequency data on an X-axis logarithmic scale, and amplitude and phase data in logarithmic or linear format on the Y-axis scale. However, most network analyzers’ input ports typically present fixed, low impedances of either 50 or 75Ω that load any device under test that connects to the ports. To measure passive or active circuits in environments other than 50 or 75Ω, you can buffer the analyzer’s inputs with amplifiers that present high input impedances to the device under test and low output impedances that match thenetwork analyzer’s inputs.

As an alternative to building or purchasing custom buffer amplifiers, you can use the near-ideal amplifiers in an analog oscilloscope that provides a vertical amplifier output on its rear panels—for example, the venerable Tektronix (www.tektronix.com) 465B. Its more commonly available cousin, the Tektronix 2465, provides a Channel 2 output on its rear panel. This Design Idea describes a proven measurement method that obtains magnitude and phase graphs of both active and passive devices. A Bode plot displays the magnitude |T(jω)| as a functionof angular frequency,ω=2πf.

Most measurements span a broad range of frequencies, and it is thus helpful to present the frequency data in logarithmic format (log f) on the graph’s abscissa (X axis), and the amplitude data formatted as 20log (|T(jω)|) on the ordinate (Y axis). Two graphs of magnitude and phase versus frequency thus present a compact representation of the network’s electrical characteristics. Using the analyzer’s controls, select the magnitude of S21 and phase of S21 as Y-axis displays in rectangular coordinates and select the log f displayoption for the X axis.

A Tektronix 465B or 2465 oscilloscope’s vertical amplifier presents a 100-MHz bandwidth, a 1-MΩ input impedance, and a 50Ω output impedance. Connect the scope’s low-impedance output to the network analyzer’s Port 2 input. A 10Χ probe that connects to the oscilloscope can raise its effective input impedance to as high as 10 MΩ. Oscilloscopes other than those mentioned—or stand-alone amplifiers—can deliver wider bandwidths, higher dynamic-input-voltage range, and reduced phase error and group delay for more accurate measurements. Figure 1 illustrates the basic measurement configuration. Use coaxial cables with appropriate connectors to match the network analyzer’s inputs. If the network analyzer requires dc bias for Port 1, use anexternal power supply.

For best results, calibrate the systemas follows.

1. Perform the network analyzer’s two-port calibration procedure over the frequency range of interest.
2. Set the network analyzer to produce a dual display, with the magnitude of S21 on top and phase of S21 at the bottom of the display screen. Change the frequency-display mode from linear to log.
3. Set the oscilloscope for dc coupling and center its trace at midscreen. Select the required sweep rate and the triggering mode to ac and adjust the trigger level to produce a trace.
4. Connect the oscilloscope’s Channel 2 input or probe to the network analyzer’s Port 1 input and set the analyzer’s controls to establish a reference line.
5. Adjust the vertical amplifier’s gain and attenuation (volts/division) controls until the analyzer displays random noise, which represents the lowest detectable signal.
6. Set the analyzer’s gain-per-division scale to 3 dB/division, a convenient value for determining the frequencies at which the gain of the device under test decreases by 3 dB.
7. Adjust the network analyzer’s source (output) power range in decibels referred to milliwatts, and the oscilloscope’s gain/attenuation settings in volts per division, to obtain an optimum data display. If the device under test introduces appreciable gain or loss, adjust the analyzer’s scale-reference control to recenter the displayed trace. Figure 2 shows a Bode plot derived from an active device that would not tolerate analyzer loads of less than 10-kΩ impedances.

To minimize the phase shift that the oscilloscope’s vertical amplifier introduces, choose an amplifier whose bandwidth greatly exceeds the operational bandwidth. In Figure 2, a vertical amplifier with a 100-MHz bandwidth fairly accurately measures a device under test operating at 10 MHz. You can eliminate phase-shift and amplitude errors that the test fixture introduces by storing a reference trace and subtracting it from the active trace. Refer to the network analyzer’soperating manual for details.