Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes Application Note

Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes Application Note Products: R&S RTO2002 R&S RTO2004 R&S RTO2012 R&S RTO2014 R&S RTO2022 R&S RTO2024 R&S RTO2044 R&S RTO2064 This application note describes how to use the R&S RTO oscilloscopes for gain and phase measurements (Bode plots) on active and passive single-ended 2-port circuits. Note: Please find the most up-to-date document on our homepage http://www.rohde schwarz.com/appnote/1td07 This document is complemented by software. The software may be updated even if the version of the document remains unchanged Application Note M. Wollinger, J. Ganzert 11.2017 1TD07_1e

Table of Contents Table of Contents 1 Overview... 3 2 Features... 4 2.1 Functionalities... 4 2.1.1 Measurements... 4 2.1.2 Results Documentation... 5 2.2 Benefit of an Oscilloscope-based solution... 5 2.2.1 Non 50 Ohm condition... 5 2.2.2 Frequency Range down to DC... 5 3 Application Examples... 6 4 Hardware Configuration... 7 5 Installation Guide... 8 5.1 Installation on the Oscilloscope RTO... 8 5.1.1 Installation Step by Step... 8 5.1.2 Attach Icon to the App Cockpit... 8 5.2 Installation on a Separate Computer...10 5.2.1 Installation location...10 5.2.2 Launching the application...10 6 Example Measurement of a Low Pass Filter... 11 6.1 Measurement Setup...11 6.2 Measurement Procedure...14 6.3 Measurement Results...15 7 Parameter Description with Ranges... 20 8 Literature... 21 9 Ordering Information... 22 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 2

Overview 1 Overview Analyzing the frequency response of active or passive components and modules is the typical application for network analyzers. However, these specialized instruments typically do not support measurements close to DC signals. Moreover, they mostly require 50-Ohm impedance. This application note describes a software supported oscilloscope-based solution, which addresses some of the above shortcomings: Not bound to 50-Ohm reference impedance. Lower frequency limit is 0 Hz. Oscilloscope probes impose only small loading on the circuit. The results are frequency response diagrams in magnitude and phase, also known as Bode plots. Surely, this approach also has some limitations: Measurement accuracy is limited due to simple error correction mechanism (no full two-port error correction like on a vector network analyzer). Frequency range determined by oscilloscope bandwidth and function generator, which is typically lower than on a vector network analyzer. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 3

Features 2 Features 2.1 Functionalities The low frequency network analyzer application allows you to characterize the frequency response of a 2-port circuit. This can be a passive component (filter, attenuator, cable) or an active component (amplifier). It is very common to move the reference plane for the measurements to the connectors of the DUT. On network analyzers, this task is called calibration or system error correction. This application also provides a simplified calibration. The software allows you to correct for phase and gain response of the cabling by means of a normalization. 2.1.1 Measurements The present application allows measuring the following characteristics: Gain response Phase response The most common measurement is the gain behavior over frequency. For filter components, the gain should be flat in the pass-band. The roll-off behavior is also important, because it influences the settling behavior (rise time, overshoot, ringing) of digital signals. Fig. 2-1: Gain response of a low pass filter Phase behavior over frequency is equally substantial. In the pass-band, the ideal phase behavior is linear over frequency. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 4

Features Fig. 2-2: Phase response of a low-pass filter Note that phase wrapping is always enabled in this software. 2.1.2 Results Documentation Documenting the measurements is always an important part of the analysis. This application offers the following features: Linear / logarithmic display of the frequency axis Note that the interval between frequency points is always linear. Save measurement to memory for direct comparison on the screen Save trace data to file Up to 4 markers In addition, the display includes some useful status information (calibration valid; count of traces in memory). 2.2 Benefit of an Oscilloscope-based solution 2.2.1 Non 50 Ohm condition Dedicated network analyzers are limited to a certain reference impedance. This is typically 50 Ohm, sometimes 75 Ohm. For any other impedance, transformers are required. The oscilloscope-based solution offers the advantage that probes have typically a high input impedance and thus impose only a small loading onto the DUT. 2.2.2 Frequency Range down to DC Network analyzers typically use directional couplers to measure all 4 S-parameters of a two-port module. Depending on the architecture of the couplers, they have a lower frequency limit of 9 khz and higher. This means that frequency response measurements cannot be done below this limit. The oscilloscope on the contrary can do measurements starting at DC. This can be a significant advantage. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 5

Application Examples 3 Application Examples The following application scenarios can be addressed with the present application: Bode plots: Gain and phase response of components / modules S-parameters: S21, S12 With couplers you can also determine S11, S22 (currently not implemented in the software) Here is a list of common types of DUTs: Filter Amplifier Attenuator Cables Fig. 3-1: Block diagram of measurement setup with optional couplers 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 6

Hardware Configuration 4 Hardware Configuration The following components are required for the application described in this document: Oscilloscope: RTO2000 Hardware options: Arbitrary waveform generator RTO-B6 Software options: RTO-K11 (IQ data software interface) Probes: All available probes can be used (passive and active probes) 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 7

Installation Guide 5 Installation Guide 5.1 Installation on the Oscilloscope RTO 5.1.1 Installation Step by Step The application comes in a standalone executable file LFNWA.exe, which launches the Low Frequency Network Analyzer. The executable file does require installation; simply save it in a location of your choice on the instrument's internal hard drive. We recommend saving the executable file in a reasonable location, like a separate folder on the desktop or in the program files directory. 5.1.2 Attach Icon to the App Cockpit The user interface of the RTO2000 allows inserting custom applications to the app cockpit. This facilitates their launch and enhances the user-friendly environment. In order to add the Low Frequency Network Analyzer application to the App Cockpit into the section User Apps, execute the following steps: Click on the menu button to open the App Cockpit Change to the User Apps tab in the App Cockpit (Fig. 5-1). Fig. 5-1: App Cockpit with the tab "User Apps" Click the "Add tool" button (Fig. 5-1) to add the desired user-defined tool shortcut to the tab. Enter the desired tool name, for example LFNWA (Low Frequency Network Analyzer) into the first textbox. (Fig. 5-2). This indication will appear later as a description below the application icon. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 8

Installation Guide Select an appropriate image by entering the path to the icon file in the respective line. Click on the " " button to open a popup window where you select the path to the icon file. You can find a suitable icon file in the installation package. Fig. 5-2: Input box to add the shortcut Now select the executable file by clicking on the " " button in the "Select tool:" line. This application does not require arguments, so leave the respective field empty. Click the "test run" to verify if the application starts correctly. (Fig. 5-2) Finally click the "Add tool" button to complete the process (Fig. 5-3). The shortcut is now visible in the App Cockpit and you can launch the application from here. Fig. 5-3: Shortcut of the LFNWA application in the "User Apps" tab 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 9

Installation Guide 5.2 Installation on a Separate Computer 5.2.1 Installation location Beside the deployment of the application on the oscilloscope itself, it is also possible to run the Low Frequency Network Analyzer on a separate computer. The installation is identical to the installation on the oscilloscope. The distributed executable file, LFNWA.exe, should be located in a reasonable location. To launch the application, the executable simply double click on the respective icon. 5.2.2 Launching the application Starting the application from the computer requires an additional step. You must first establish a connection to the oscilloscope. At the launch of the executable file, a popup window requests the IP address of the device. You can enter the computer name (hostname) of the oscilloscope as well as the IP address. The application terminates automatically, upon entering an incorrect IP address or connection failure. For a second try, restart the executable file LFNWA.exe. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 10

Example Measurement of a Low Pass Filter 6 Example Measurement of a Low Pass Filter 6.1 Measurement Setup The characterization of a low pass filter will clarify the measurement procedure and its setup. Connect the measurement points of the DUT channel 1 and 2 of the oscilloscope. Note that the measuring probe of channel 1 shall be connected exclusively to the input port of the DUT and the probe of channel 2 to the output port of the DUT (Fig. 6-1). This is due to the assumption of the application that channel 1 measures the signal at input side and channel 2 on output side. Fig. 6-1: Connection of the oscilloscope channels for S21 measurement Fig. 6-2: ARB signal generator output on the rear panel In order to measure the S21 forward transmission parameter, a sine wave from the internal generator of the oscilloscope is applied to the DUT. The output of the DUT 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 11

Example Measurement of a Low Pass Filter shall be terminated with the matching impedance of the DUT (typically 50 ohms) to avoid reflections. The output Gen 1 of the RTO-B6 option at the back of the oscilloscope is connected to port 1 of the DUT with a BNC cable. Output Gen 2 can also be used; in this case, the setting needs to be adapted in the menu of the user interface of the application. Port 2 of the DUT is terminated with a 50-Ohm resistor. The various parameters for the measurement are entered in the user interface. The default arguments are displayed in Fig. 6-3. For the characterization of the example low pass filter, the frequency should sweep from 20 MHz to 50 MHz. Set the start frequency by clicking on the button, which displays the current frequency setting. A popup window (Fig. 6-4) enables you to insert the required value and to confirm the input with the according unit button. A step frequency of 1 MHz is a reasonable value for this measurement range. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 12

Example Measurement of a Low Pass Filter Fig. 6-3: Configuring the measurement parameters Fig. 6-4: Setting the Start Frequency The level of 0 dbm is also suitable for the low pass filter measurement. The correct input power depends on the characteristics of the DUT. For passive components (filters, attenuators) it must be sufficient to provide a signal at the output that is well above the noise floor in the passband. For amplifiers, it must be sufficiently low at the amplifier input to avoid saturation of the DUT. The dbm values are referenced to the underlying 50-Ohm system. Select the bandwidth from a drop down list. This parameter is crucial for the frequency resolution of the measurement. With a frequency range in the MHz region, the default bandwidth of 10 khz is a good choice. The average factor applies to each individual measurement point. A higher average count implies that the data is acquired multiple times at each frequency point and averaged, before displayed on the plot. Averaging has a similar effect like filtering. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 13

Example Measurement of a Low Pass Filter 6.2 Measurement Procedure Start the measurement after all settings are completed. However, depending on the connection setup of the DUT a calibration step may be useful or even required. For the calibration / normalization step, insert a through connection instead of the DUT. Start the calibration by clicking on the CAL button in the measurement group (Fig. 6-5). Fig. 6-5: Measurement section During the calibration process, the system collects data that characterizes the frequency response outside the DUT thus compensating unwanted effects in cabling and connectors. The calibration procedure will display a dotted trace, and display the valid range of the accomplished calibration in the "Info" section on the user interface (Fig. 6-7). Modifying the frequency range (start and stop frequency) results in cancellation of the calibration. Fig. 6-6: Info section 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 14

Example Measurement of a Low Pass Filter Fig. 6-7: Dotted graph displays the calibration After performing the calibration, connect the DUT to the measurement setup. Start the actual measurement by clicking on the Start button in the measurement section on the user interface (Fig. 6-5). The trace displays the transmission function of the device under test (DUT) in the selected frequency range. The recorded calibration values are taken into account accordingly. 6.3 Measurement Results The curves, displayed on the two bode plots; represent the transmission function, S21, of the DUT. The upper graph displays the amplitude frequency response and provides information on the amplitude behavior over the according frequency range in db (Fig. 6-8). Fig. 6-8: Gain response The second plot displays the phase characteristics over frequency, measured in (Fig. 6-9). 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 15

Example Measurement of a Low Pass Filter Fig. 6-9: Phase response You can adjust the y - axis scaling of the gain graph in the Scaling menu. The menu section provides two scaling types for the y-axis: Manual scaling: Select Scale/Div., Ref Value, and Ref Pos values manually (Fig. 6-10) Auto scaling: The vertical scale is adjusted automatically such that the graph fits entirely into the diagram. The scale/div parameter determines the db per division. The diagram always contains 10 divisions. The reference value and the reference position are auxiliary values to control the configuration of the plotting area. The reference value, marked with a blue, horizontal line, is positioned by the reference position onto a specific division. With frequency response of the low pass filter moving close to the border of the plot, it is good practice to adjust the scaling manually. To lower the plotted line, set the reference position set to a smaller value, e.g. 8. Fig. 6-10: Vertical scale setup Similar to the vertical axis, you can adjust the scaling of the frequency (x-) axis. The frequency axis can be displayed either in a linear or in a logarithmic scale. For the example of the low pass filter, the linear scale configuration is sufficient. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 16

Example Measurement of a Low Pass Filter For a better inspection of the frequency responses, several markers are available under the set marker menu. Four markers can be activated via a pop-up window. Fig. 6-11: Marker Settings Set the frequency position of the several markers by clicking on the button and entering the desired frequency value. Alternatively, you can drag the marker to the desired position, directly on the plotted trace. A legend appears above the diagrams, displaying the corresponding coordinates of the markers. To determine the cutoff frequency of the low pass filter, you can activate two markers. The cutoff frequency is defined as the frequency for which the output of the circuit is 3 db below the nominal passband value. To consider this condition, place marker 1 at the nominal passband, and marker 2, 3 db below marker 1. The marker info facilitates finding the exact position of the cutoff frequency and determine the frequency value of 24.26 MHz (Fig. 6-12). 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 17

Example Measurement of a Low Pass Filter Fig. 6-12: Marker measurements In order to compare the recoded transmission function with a transmission function from another device, the Data to Memory button (Data Mem) in the measurement region saves the current trace to a local memory. For comparison, the second DUT must be inserted into the measurement setup and measured. The local data will be plotted concurrently. You can compare several traces with this feature. The following figure 6-10 displays the comparison of the low pass filter of the example, and a high pass filter with a cut off frequency at the same frequency. The red, dotted trace represents the local stored frequency response of the low pass filter. The high pass filter frequency response got loaded by the menu option, read data from file. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 18

Example Measurement of a Low Pass Filter Fig. 6-13: Comparing a low-pass filter and a high-pass filter Another benefit of this option is shown in Fig. 6-14. The red-dotted race displays the locally saved low pass filter. The new measured trace is the same filter with an in series connected attenuator. It can be observed that the additional component attenuates the amplitude frequency response by 10 db. Fig. 6-14: Low-pass filter with additional attenuator 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 19

Parameter Description with Ranges 7 Parameter Description with Ranges Parameter Description Range Start Frequency upper range limited by current Stop 1Hz to 100MHz Frequency Stop Frequency lower range limited by current Start 1 Hz to 100 MHz Frequency Step Frequency Linear interval between frequency 1 Hz to 100 MHz points Level ARB generator output level (=DUT -35dBm to 19dBm input level) Bandwidth Filter bandwidth 1kHz, 2kHz, 4kHz, 5kHz, 10kHz, 20kHz, 40kHz, 50kHz, 100kHz Average Averaging factor for point average at each frequency point Integer value from 1 to 1000 Scale per Vertical scale 0.5 db/div to 20 db/div division Reference Vertical reference value -100 db to 100 db Value Reference Position Vertical reference position 0 to 10 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 20

Literature 8 Literature [1] <Autor> <Title> (Enter Bibliography via >R&S Manual!Figure+Tools >Manage Bibliography Sources, In dialog: activate "Show All Bibliography Fields" to enter hyperlinks) [Book Section]. - <Year>. 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 21

Ordering Information 9 Ordering Information Naming Type Order number Digital Oscilloscopes 600 MHz, 2 channels 10 Gsample/s, 50/100 Msample 600 MHz, 4 channels 10 Gsample/s, 50/200 Msample 1 GHz, 2 channels 10 Gsample/s, 50/100 Msample 1 GHz, 4 channels 10 Gsample/s, 50/200 Msample 2 GHz, 2 channels 10 Gsample/s, 50/100 Msample 2 GHz, 4 channels 10 Gsample/s, 50/200 Msample 3 GHz, 2 channels 10 Gsample/s, 50/100 Msample 3 GHz, 4 channels 10 Gsample/s, 50/200 Msample 4 GHz, 4 channels 10 Gsample/s, 50/200 Msample 20 Gsample/s, 50/100 Msample 6 GHz, 4 channels 10 Gsample/s, 50/200 Msample 20 Gsample/s, 50/100 Msample Hardware Options R&S RTO2002 1329.7002.02 R&S RTO2004 1329.7002.04 R&S RTO2012 1329.7002.12 R&S RTO2014 1329.7002.14 R&S RTO2022 1329.7002.22 R&S RTO2024 1329.7002.24 R&S RTO2032 1329.7002.22 R&S RTO2034 1329.7002.24 R&S RTO2044 1329.7002.44 R&S RTO2064 1329.7002.64 Arbitrary Waveform Generator R&S RTO-B6 1329.7054.02 Software Options I/Q Software Interface R&S RTO-K11 1317.2975.02 1TD07_1e Rohde & Schwarz Analyze Frequency Response (Bode Plots) with R&S Oscilloscopes 22

Rohde & Schwarz The Rohde & Schwarz electronics group offers innovative solutions in the following business fields: test and measurement, broadcast and media, secure communications, cybersecurity, radiomonitoring and radiolocation. Founded more than 80 years ago, this independent company has an extensive sales and service network and is present in more than 70 countries. The electronics group is among the world market leaders in its established business fields. The company is headquartered in Munich, Germany. It also has regional headquarters in Singapore and Columbia, Maryland, USA, to manage its operations in these regions. Regional contact Europe, Africa, Middle East +49 89 4129 12345 customersupport@rohde-schwarz.com North America 1 888 TEST RSA (1 888 837 87 72) customer.support@rsa.rohde-schwarz.com Latin America +1 410 910 79 88 customersupport.la@rohde-schwarz.com Asia Pacific +65 65 13 04 88 customersupport.asia@rohde-schwarz.com China +86 800 810 82 28 +86 400 650 58 96 customersupport.china@rohde-schwarz.com Sustainable product design Environmental compatibility and eco-footprint Energy efficiency and low emissions Longevity and optimized total cost of ownership This application note and the supplied programs may only be used subject to the conditions of use set forth in the download area of the Rohde & Schwarz website. R&S is a registered trademark of Rohde & Schwarz GmbH & Co. KG; Trade names are trademarks of the owners. PAD-T-M: 3573.7380.02/02.05/EN/ Rohde & Schwarz GmbH & Co. KG Mühldorfstraße 15 81671 Munich, Germany Phone + 49 89 4129-0 Fax + 49 89 4129 13777 www.rohde-schwarz.com