A Bode plot can ease characterisation 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 analysers' 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 analyser's inputs with amplifiers that present high input impedances to the device under test and low output impedances that match the network analyser's inputs. As an alternative to building or purchasing custom buffer amplifiers, you can use the near-ideal amplifiers in an analogue oscilloscope that provides a vertical amplifier output on its rear panels—for example, the venerable Tektronix 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 function of 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 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 analyser's controls, select the magnitude of S21 and phase of S21 as Y-axis displays in rectangular coordinates and select the log f display option for the X axis.

EDNAOL 2016JUN14 AN 01Fig1Figure 1: The basic test setup for generating Bode plots requires a network analyser, an analogue oscilloscope with one or more vertical outputs, an optional dc-bias power supply, and a printer. A Tektronix 465B or 2465 oscilloscope's vertical amplifier presents a 100MHz bandwidth, a 1-MΩ input impedance, and a 50Ω output impedance. Connect the scope's low-impedance output to the network analyser's Port 2 input. A 10× 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 analyser's inputs. If the network analyser requires dc bias for Port 1, use an external power supply. For best results, calibrate the system as follows. Perform the network analyser's two-port calibration procedure over the frequency range of interest.Set the network analyser 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.Set the oscilloscope for dc coupling and centre its trace at midscreen. Select the required sweep rate and the triggering mode to ac and adjust the trigger level to produce a trace.Connect the oscilloscope's Channel 2 input or probe to the network analyser's Port 1 input and set the analyser's controls to establish a reference line.Adjust the vertical amplifier's gain and attenuation (volts/division) controls until the analyser displays random noise, which represents the lowest detectable signal.Set the analyser'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.Adjust the network analyser'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 analyser's scale-reference control to recenter the displayed trace. Figure 2 shows a Bode plot derived from an active device that would not tolerate analyser loads of less than 10-kΩ impedances.

EDNAOL 2016JUN14 AN 01Fig2Figure 2: A vertical amplifier with 100MHz bandwidth fairly accurately measures a device under test operating at 10MHz, plotting the magnitude (top-trace) behaviour and phase (bottom-trace) behaviour of a typical device in log-frequency format spanning a 50kHz to 15MHz range. Markers show measured values at reference points.

To minimise 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 100MHz bandwidth fairly accurately measures a device under test operating at 10MHz. 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 analyser's operating manual for details.
This article is a Design Idea selected for re-publication by the editors. It was first published on March 29, 2007 in EDN.com.