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Application Note Intermodulation Distortion Intermodulation Distortion Measurements on Modern Spectrum Analyzers Application Note Products: | R&SFSV | R&SFSW This Application Note describes the differences in intermodulation distortion measurements between traditional spectrum analyzers with analog narrow- band IF signal path and modern spectrum analyzers using a wide-band IF signal path and digital RBW filters. _2E 79 1EF – Application Application Note Dr. Florian Ramian June 2012 Table of Contents Table of Contents 1 Introduction ............................................................................ 3 2 Intermodulation Distortion .................................................... 3 2.1 Harmonic signals ......................................................................................... 3 2.2 Intermodulation as a result of harmonic signals ...................................... 4 2.3 Characterizing IMD ....................................................................................... 4 3 Comparison of Architectures ................................................ 7 3.1 Traditional swept spectrum analyzers ....................................................... 7 3.2 Modern wide-band (signal- and) spectrum analyzers .............................. 8 3.3 Comparison .................................................................................................10 3.4 Impact of electronic attenuators and RF preamplifiers ..........................12 4 Measurement of Intermodulation Distortion ...................... 14 4.1 Measurement setup ....................................................................................14 4.2 Generator influence ...................................................................................14 4.3 Spectrum analyzer influence .....................................................................15 4.3.1 RF preamplifier and electronic attenuator ...............................................15 4.3.2 Mixer stage influence .................................................................................15 4.3.3 Noise floor influence ..................................................................................16 4.3.4 ADC influence .............................................................................................16 4.3.5 Finding the ideal mixer level .....................................................................17 5 Ordering Information ........................................................... 20 1EF79_1E Rohde & Schwarz Intermodulation Distortion Measurements on Modern Spectrum Analyzers 2 Introduction Harmonic signals 1 Introduction Intermodulation distortion (IMD) plays an important role for many spectrum analyzer based measurements. Mostly spectrum analyzers are used to measure IMD of a Device Under Test (DUT). However, a spectrum analyzer may also contribute to IMD due to the non-linear behavior of its different active components used in its signal path. The most critical intermodulation distortion product is the Third Order Intermodulation (TOI) product. It is generated when two signals are applied to a nonlinear device. The TOI products are usually within or close to the use-band, i.e. it can hit a neighboring channel in a communication system. This application note gives an overview which elements contribute. It also includes recommendations for the optimum level setting to minimize spectrum analyzer generated IMD. Chapter 2 explains the theoretical background of intermodulation distortion in more detail. Chapter 3 compares the differences in architecture between the analog narrow-band spectrum analyzer approach and a modern wide-band signal- and spectrum-analyzer. Chapter 4 focuses on TOI measurements of a DUT in practice. A typical measurement setup is shown and the influence of signal generators and the spectrum analyzer on the measurement is explained. This chapter also gives recommendations how to avoid measurement errors resulting from intermodulation products of the signal generators or spectrum analyzers. Readers who are interested in a guideline on how to obtain accurate IMD measurement results are welcome to proceed directly to chapter 4. 2 Intermodulation Distortion Intermodulation distortion originates from non-linearities in electronic circuits. Non- linear elements generate harmonic signals, or in more detail: non-linear elements create signals at multiples of the input signal. Chapter 2.1 describes the mathematical background on harmonic signals caused by non-linear elements, whereas chapter 2.2 introduces intermodulation as a result of harmonics from non CW signals. 2.1 Harmonic signals This section will show the basic equations for harmonics created in a single tone scenario. Given the case that a single CW tone is applied to a non-linear element, additional signals, the so-called harmonics, will be generated at n times of the original frequency, with n being the order of the harmonic. Any non-linear element can be described by a Taylor-series 2 3 (1) Ps a0 a1 s a2 s a3 s with P(s) being its transfer function and s being the input signal. We will not look in detail on the factors an, but focus on the powers of s. Assuming a CW input signal, the general formula for a signal s as a function of time t is 1EF79_1E Rohde & Schwarz Intermodulation Distortion Measurements on Modern Spectrum Analyzers 3 Intermodulation Distortion Intermodulation as a result of harmonic signals st B cos2 f t . (2) Using the addition theorem for the cosine function, it is straight forward to figure out that the square term in Eq. (1) creates a signal with twice the original frequency (the second harmonic), the cube term the third harmonic and so on. For a more detailed explanation of these formulas, please refer to the Rohde & Schwarz Application Note 1EF78, or the internet. 2.2 Intermodulation as a result of harmonic signals Clearly, harmonics of a single tone are outside the usable band of an application, since they are at multiples of the original frequency. Once a second tone joins the input signal at a small frequency offset – the resulting output signal looks different. In contrast to the single tone scenario above, the signal s is now (3) st B1 cos2 f1 t 1 B2 cos2 f 2 t 2 . Since the dominating intermodulation products are the third order products, the following equations focus only on those. Calculating the third power terms (responsible for the third order intermodulation and third order harmonics) of the Taylor series (Eq. 1) with the two tone input signal from Eq. 3 yields the following result: 3 3 3 (4) s (t) B1 cos 2 f1 t 1 3 3 B2 cos 2 f 2 t 2 2 2 3 B1 B2 cos 2 f1 t 1 cos2 f 2 t 2 2 2 3 B1 B2 cos2 f1 t 1 cos 2 f 2 t 2 The first two lines describes the third order harmonics for each of the input tones (cos3-terms), whereas lines 3 and 4 represent the third order intermodulation terms (mixed terms). From the above equations, the TOI frequencies can be derived using the addition theorem (for trigonometric functions) as f 2 f f (5) TOI1 1 2 . f TOI2 2 f 2 f1 rd While the 3 order harmonics ( 3 f1 and 3 f 2 ) of the individual input tones can be easily suppressed by a low-pass filter, the third order intermodulation terms are often more critical for the application. The resulting frequencies are often in-band for a given application and therefore interfere with the wanted signal. Additionally, under the assumption B1 = B2, i.e. both tones have the same level, the intermodulation terms exceed the harmonic terms by a factor of 3 in amplitude (Eq. 4). A factor of 3 in amplitude converts to a 9.54 dB difference between the third order harmonics of the individual tones and the third order intermodulation products. 2.3 Characterizing IMD There is a number of ways to visualize intermodulation distortion. Fortunately, the measurement method is identical and the results can be converted. 1EF79_1E Rohde & Schwarz Intermodulation Distortion Measurements on Modern Spectrum Analyzers 4 Intermodulation Distortion Characterizing IMD The measurement method used to characterize the IMD behavior of a DUT is the so- called two tone scenario. Two continuous wave (CW) tones with equal tone power (PInTone) and spaced by a given frequency (Δf) are applied to the DUT input (see Figure 1). On the output side, the power level of the original tones may have changed to PTone. The intermodulation products can be measured with their absolute power or their relative power related to PTone, referred to as PΔ. In practice PΔ is also called intermodulation free dynamic range. Clearly, the 3rd order intermodulation tones have the same spacing to the upper and lower tone as the two original tones have (Δf). PΔ PTone PIM3 Δf Δf Δf Figure 1: Two tone scenario used for IMD testing Additionally, the so-called third order intercept point (IP3) can be calculated. It is a theoretical point, where the intermodulation products at the DUT’s output grow as large as the original tones at the DUT output side. The IP3 can be derived on a logarithmic scale (i.e. all values in dBm or dB) as (6) IP3 PTone P / 2 . Figure 2 shows graphically the relation of Eq. 6. It shows the theoretical lines of the fundamental and 3rd harmonic at the output of a 0 dB gain DUT. 1EF79_1E Rohde & Schwarz Intermodulation Distortion Measurements on Modern Spectrum Analyzers 5 Intermodulation Distortion Characterizing IMD 80 Fundamental 3rd Harmonic 60 40 IP3 20 / dBm / P Tone output P 0 P =P +P /2 IP3 Tone -20 P -40 -60 -60 -40 -20 0 20 40 60 80 P / dBm InTone Figure 2: Graphical representation of
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