Solution: First the VSWR figures are converted to reflection coefficient magnitudes: Then the mismatch uncertainty is: M u = ±200 (0. Calculates Radar Doppler shift, with speed, height and distance as input parameters. Conducted Immunity calculator; Radiated Immunity calculator; SAR calculator; TEM cell calculator; Strip line calculator; Filters. Calculates Butterworth response analog filters up to the 9th order. The main cause of the mismatch is the deviation in the con-VSWR (Voltage Standing Wave Ratio) is a measurement of how well matched a radio transmitter and transmission line is to a load such as an antenna. Enter the Noise Figure and gain for each stage. 01. ,100 % power transferred from a source to a load via a transmission line/cable). Wavelength Calculator. Types of quadrature couplers include branchline couplers (also known as quadrature hybrid couplers), Lange couplers and overlay couplers. Because the reflection coefficient Γ < 1, then the return loss will have a positive dB value. This makes the amplifier less efficient. Reflection Conversion Table: To provide the correlative value of VSWR, Return Loss, Reflected Power, Reflection Coefficient. 0. The operating frequency. 8:1 (10. From a system VSWR level calculate the following parameters: - Reflection coefficient. As an added bonus, the. An amplifier usually provides a constant gain over a specific frequency range. This Javascript calculator converts between return loss (RL), voltage standing wave ration (VSWR), and reflection coefficient (Γ). Wire over Ground Calculator. Right-Hand Rule. - Forward and reflected power percentage. It is a measure of how efficiently RF power is transmitted from the power source, through a transmission line, and into the load. The trick here is to figure out what the total gamma is. The following table provides conversions for wavelength (from frequency), VSWR (from forward and reflected power). Coaxial Cable Cutoff Frequency Calculator. of the filter. Propagation time/distance Calculator For a given medium dielectric, calculate propagation distance for a set time and vice versa. Resistor Values. VSWR and its Effects on Power Amplifiers. Some are based on look-up tables, some completely hide their algorithms. Reflection Coefficient / VSWR / Return Loss. It uses a bilinear Moebius transformation, projecting the complex impedance plane onto the complex Γ plane: Γ = Z −Z0 Z +Z0 with Z = R +jX (3) As can be seen in Fig. Read his latest diatribe here, or visit the amazing Unknown Editor's Archives when you're looking for a. From Fig. 5 * 2. Microstrip. com . 05+j51. Determining the noise and distortion as a progression through the RF chain is known as cascade analysis. This white paper will give you a brief overview on the history of VSWR, as well an some information on short-circuit and open-circuit termination and the creation of standing waves. VSWR is defined as the ratio of the maximum voltage to the minimum voltage in standing wave pattern along the length of a transmission line structure. Here are the things that you can plot in this version. - Tee Attenuator Calculator. in a rectangular waveguide has been presented based on Mode Matching Technique. Large selection of online interactive calculators for RF design, including attenuators, capacitance, resonance, RF traps, and microstrip impedance. RF Cascade Workbook for Excel. Even though the effect of VSWR interactions between stages is not included when performing the calculations, the results are a good first order approximation of the cascaded performance of the. Stripline Calculator. Cascaded Noise Figure calculator Chebyshev filter designer Coplanar GB waveguide calculator. This is a required field. More details for 85059B can be seen below. Voltage Standing Wave Ratio (VSWR) is defined as the ratio of the maximum to the minimum voltage on a loss-less line. Maximize Bandwidth for cascaded Opamps; Slew-Rate Considerations;. Post subject: Cascaded RL Calculations? Unread postPosted: Wed Aug 11, 2004 5:13 pm . RF & Electronics Symbols for Visio. Specify the bandwidth and SNR and Noise Factor ( Set noise factor) to obtain the sensitivity in dBm or dBuV (50 Ohms). I am using the specified max VSWR. To do it properly and exactly, look up S parameters in wikipedia here, and go to section 'S-parameters in amplifier design', where it gives the expression for how to determine the total reflection coefficient of a cascade of two systems from their S-parameters. Studying the graphs, it is apparent that this simple circuit performs well over 20% bandwidth. 0. VSWR Return Loss. Mismatch loss should be minimized in cascaded RF system calculations and can represent a significant loss of power delivered to the antenna. This equation gives the method for calculating cascaded NF (nf) values based on the nf and gain. This is a required field. Resonators (λ/4-Wave Coaxial) Return Loss / VSWR / Gamma. The table shows the effects of combining two components in terms of their maximum VSWR and return loss. Following equation or formula is used for Horn Antenna calculator. Solution: First the VSWR figures are converted to reflection coefficient magnitudes: Then the mismatch uncertainty is: M u = ±200 (0. These are the standard set of equations for converting between VSWR, return loss, and reflection coefficient (Γ). The calculated value is MUCH worse. The easiest way to improve return loss is to add an attenuator. The calculated value is MUCH worse. = reflected power. Enter the two antenna heights in meters, feet, kilometers or miles and read the maximum range (r) between the antennas also in meters, feet, kilometers or miles. Antenna Downtilt Calculator. 64/100) = ±0. RF Calculator: Wavelength, dBm, dBuV, W, dBuV/m, mW/cm^2, pJ/cm^2, V & VSWR This RF calculator has been developed by Compliance Engineering as a resource for individuals involved in EMC and RF compliance measurements. Thus, for this system, VSWR = 1:1 (i. Unit Converters. Note that the VSWR and reflection coefficient are just different ways to represent return-loss. Transmit and receive antenna gains (Gtx & Grx). 2 wavelengths from the load The magnitude of the reflection coefficient at the load is MagΓL≔――― VSWR−1 VSWR+1 and the phase of the reflection coefficient is ΦΓL≔−⎛⎝π+4⋅π⋅zmin ⎞⎠ Therefore, the normalized load impedance isPI Attenuator Calculator. VSWR values were used to calculate the other. Expressed as 3. =Γ2 = 10−RL/10 = Γ 2 = 10 − R L / 10. However, convention and some literature quote return loss as a negative value akin to an S (1,1) measurement on a Network. The result will appear below. The V03CAL Series from OML Inc. 8 dB RL TMA) Then: X (max) = 1. VSWR is determined from the voltage measured along a transmission line leading to an antenna. 1) Introduction. Pincident watts. VSWR is defined as the ratio of the maximum to minimum voltage on a loss-less transmission line (expressed as 3. , the signal reflected back in a transmission line. Zero . 01. The table was created with a handy Windows-based program called VSWR Calculator, detailed by author Steve Hageman of Agilent Technologies (Santa Rosa, CA) in his articleVSWR (pronounced "viswar"), or the Voltage Standing Wave Ratio, is the ratio of the maximum standing wave amplitude at one node to the minimum amplitude at another node in a system. Voltage standing wave ratio (VSWR) is defined as the ratio between transmitted and reflected voltage standing waves in a radio frequency (RF) electrical transmission system. 5) best case if the reflected. ocx这个插件才能运行上面的这个功能. This can be built into a FLEXI-BOX and a transmission line (50 Ohm track) PCB is available which easily adapts for this circuit with one simple trimming. —and. The V05CAL Series from OML Inc. WinRFCalc download page. 在Windows 10系统中, 这个还需要额外配置mscomctl. The Unknown Editor has been spouting off about a variety of topics since he started this site back in 2001. a = outside radius of inner conductor (inches) b = inside radius of outer conductor (inches) c = speed of light in a vacuum = 299,792 km/s = 186,282 mi/s. The concept behind the Smith Chart is simple. ε = dielectric constant = ε0 * εr. A key parameter of amplitude and phase control products is the. Please. 011. Interactive Tools & Calculators. Mismatch Loss (dB) 3. A quadrature coupler is one in which the input is split into two signals (usually with a goal of equal magnitudes) that are 90 degrees apart in phase. NEW Version V2323, released on 31 May 2023, FREE DOWNLOAD, WinRFCalc is the best Windows RF calculator toolbox for EMC, RF and Radio engineers. Useful converters and calculatorsTwo years ago, one of our most respected RF experts, Lou Meyer, wrote a blog post describing the technicalities of return loss and voltage standing wave ratio (VSWR) and how the multiple components at a cell site tower make the calculations more complex. 5:1 equates to a Return Loss of 13. If we represent the Input power Vs Output power of an amplifier on a graph, we get a straight line (Linear Relationship) i. 01 November 2023, 18:15 CEST. VSWR/Return loss converter Wavelength calculator Wilkinson splitter designer. Where, RL = Return loss in dB. Unless you have a piece of slotted line-test equipment this is a hard definition to use, especially since the concept of voltage. VSWR can be generated by Network Analysers. To use the calculator below, input a values into the fields and hit the enter key. Enter the sample rate of the ADC (Fsamp), Spurious (Fspur) and optionally adjust the maximum frequency to calculate to (Fmax). Enter the Noise Figure and gain for each stage. ; Please Support RF Cafe by purchasing my ridiculously low−priced products, all of which I created. Conversions: nf = 10 NF/10 ↔ NF (dB) = 10 * log 10 (nf) where nf is a unitless ratio and NF has units of dB. Calculates the resistor values, attenuation, minimum attenuation, 'impedance', reflection coefficient, VSWR and return loss of a matching Pi attenuator. RF Cascade Workbook for Excel. If there is something in the microwave universe that you need a different calculator for, drop us a note and we'll see what we can. Here is a list of some of the calculators in this app: Attenuator Calculators. Amateur Radio AstronomyReflection coefficient (Γ) is the fraction of a forward traveling wave that is reflected from a mismatched load, expressed in polar coordinates (|Γ| (θ). g. This article offers an introduction to the Smith chart and how it’s used to make transmission-line calculations and fundamental impedance-matching circuits. There are a variety of different types of gain equalizers, a common circuit type is a frequency variable attenuator, which equalizes gain by having a slope which complements the sloping gain of the original circuit. Bandwidth. Resistor Markings & Color Codes. Cascaded Noise Figure calculator Chebyshev filter designer Coplanar GB waveguide calculator C-Coupled Resonator designer. Forward Power (W) Reverse Power (W) VSWR. 009 Mismatch Loss (dB). VSWR (Voltage Standing Wave Ratio) and Return Loss both measure the same parameter i. - Mismatch loss in dB. VSWR Calculator. Continuing the tradition, RF Cafe Espresso Engineering Workbook™ is also provided at no cost. No:35/109 Golbasi Ankara/TURKEYConvenient for describing this distribution is the voltage standing wave ratio (VSWR), defined as the ratio of the maximum voltage amplitude to the minimum voltage amplitude. With this calculator tool you can calculate the resonance frequency of a a cavity ( rectangular or cylindrical ) and a structure on a PCB. comRF Trap With Attenuator Calculator Calculates the attenuation, 'impedance', reflection coefficient, VSWR and return loss of a circuit that incorporates a RF tank circuit into a Pi attenuator. VSWR=(1+ρ)/(1-ρ) For cases where Z L is real, with a little algebra you'll see there are two cases for VSWR, calculated from load impedance: For Z L <Z 0: VSWR=Z 0 /Z L. The gain uncertainty arises due to impedance mismatch between the device and another connected device (e. This impedance incongruity leads to the performance deterioration in active device parameters such as efficiency, gain etc. Joined: Wed Aug 11, 2004 5:11 pm. It is explained here. Given the parameters above, this tool provides the power at the receive and. Visit Pasternack's RF amplifiers page for product details. RLC Combinations:. Resistivity. With this tool, you can calculate the filter taps (coefficients) of four types Kaiser-Bessel FIR ( F inite I mpulse R esponse) digital filters: depending on the sampling rate, number of taps and attenuation levels. It provides a measure of how efficiently RF power is transmitted from a power source, through a transmission line, to a load such as an antenna. These multiple solutions are possible because each contributor is a vector having both. Since 2002, the original Calculator Workbook has been available as a free download. Mixer Spur SearchLink Budget is a way of quantifying a communication link's performance while accounting for the system's power, gains, and losses for both the transmitter (Tx) and receiver (Rx). Capacitor calculator; Cascaded amplifiers; Coaxial impedance; Reactance and resonance; VSWR Calculator; Wavelength and. This online VSWR Calculator is also very useful. Aug 6, 2018. Mismatch loss is the ratio of power delivered to power available, and is a simple function of reflection coefficient. What is VSWR? VSWR (Voltage Standing Wave Ratio) is the measure of how efficiently RF power is transmitted in to a load. 0 = 1. Download this article of VSWR Explained. Fortunately, Visual System Simulator (VSS) software in the AWR Design Environment platform has many measurements that assist in cascade analysis. 2:1 (20. 0x1. Here we will learn more about the meaning of VSWR and the associated VSWR formulas. A significant challenge for RF designers is the optimization of an RF chain for noise and distortion performance. You can choose different input formats from the drop down menu. Skin Depth Calculator. Consider the three cascaded amplifier stages, each amplifier stage has a noise figure of 3 dB and power gain of 10 dB, then the calculation of total noise figure is given below. - Bridged Tee Attenuator Calculator. These calculators help with unit conversions, VSWR calculations, attenuator design, antenna design, radars, and various other basic calculations that are often required. - Pi Attenuator Calculator. This VSWR calculator will calculate return loss, mismatch loss, loss in percentage and the reflection coefficient. Application Note File. In industry, VSWR is sometimes pronounced "viz-wer". Convert VSWR to Return Loss and vice versa. Learn about voltage standing wave ratio (VSWR), return loss, and mismatch loss, which helps characterize the wave reflections in a radio frequency (RF) design. It's shown in the context of the first system being an amplifier, and the second a. A SWR can be also defined as the ratio of the maximum amplitude to. RF Cascade Workbook for Excel. The noise figure number, displayed in decibels (dB), represents the performance by which an amplifier or RF receiver can be measured. VSWR Calculator Calculate voltage standing wave ratio (VSWR) and return loss for mismatched circuit. I leave it to other sources to provide the complex equations needed to precisely model coaxial cables. With this tool, the output frequencies of an RF mixer are calculated using the Henderson [see the Watkins Johnson application note written by Henderson available after the installation of WinRFCalc] model for spurious calculations. , bn). The calculated value is MUCH worse. ( 14 more products) Download Datasheet Request Quote. From the figure, following two equations are. Preferred resistor values are entered into the text boxes, similar to the way that values for a prototype may be selected. The cascaded effects of the noise figures and losses of the components following the attenuator, including the LNA, will increase the noise figure considerably beyond 3 dB,. Calculate VSWR from Forward and Reverse Power. This is equal to a return loss of 14 dB or greater. Design, development and small scale manufacture of simple RF and Audio items. 2 at 2380 MHz, the mismatch loss is calculated to be 0. VSAT Components (Satellite Communications) Sensor Modules (WaveEyes) Components for Radar, Electron Guns and Cathodes; VSAT Components (Satellite Communications) Calculator. Calculates the Free Space Transmission Loss (FSTL) between two antennas based on: Transmit power. A beautiful, free online scientific calculator with advanced features for evaluating percentages, fractions, exponential functions, logarithms, trigonometry, statistics, and more. The calculator can also be used to find the value of VSWR using any of the other values. L nH uH mH C pF nF uFCascade VSWR Back-lobe Qualifier Touch-Down Points Wavelength Calculator Free Space Loss Calculator Reflection Conversion Table dBm to Watts and Watts to dBm Convertor Please hit Thanks and add reputation if you like my post. The phase angle may be given as 0 to 360 degrees or +180 to –180 degrees, depending on the analytical. D. be used to add or subtract an arbitrary number of power, to convert power and voltage units from the linear to the logarithmic. You can also use this calculator to find out the Power Gain and Voltage Gain from the Decibel value. Fortunately, there’s a very easy way to analyze complex loads using graphical methods and it’s called the Smith Chart. AppCad Design Assistant. Return Loss (dB) VSWR Feet LDF4-50A VXL7-50 No No No No No No No No No No No Yes Yes No FSJ4-50B PRIVATE AND CONFIDENTIAL CommScope 90 Possible Cascaded VSWR Results If: L = 1. The relation between VSWR, impedance and return loss is: VSWR : Vs = Zc/Z0, if Zc, the component impedance is greater than Z0, the system characteristic impedance or, Vs = Z0/Zc, if Z0>Zc. Looking at the datapoints and moving back from the antenna (75. VSWR ( VSWR meaning Voltage Standing Wave Ratio) is an important concept in radio frequency (RF) engineering. VSWR to Return loss calculator. 25:1 (19. Our results are optimised for gain, but others may be optimised for bandwidth. This general RF calculator includes calculations of path loss, VSWR and wavelength as well as conversions between many common terms used in the wireless industry. The VSWR is a measure of the efficiency of a transmission line and is used to determine how well the line is matched to the impedance of the. VSWR (voltage. Consider the 6dB antenna return loss case. RF Calculators. This paper further validates this equation against experimental data obtained for. VSWR Conversion Table. VSWR/Return loss converter Wavelength calculator. 091) (0. I have already calculated the cascaded VSWR and RL using the RSS method (very similar result to simply multiplying each components VSWR as Itay mentioned), but the problem is that the result is not even close to the measured value of return loss. Simply select the tool that best suits your purpose. NEW Version V2323, released on 31 May 2023, FREE DOWNLOAD, WinRFCalc is the best Windows RF calculator toolbox for EMC, RF and Radio engineers. 5dB and assuming the passive mixer noise figure equals 7. Solution: Internally, this calculator first. This mismatch can influence the performance of the source. 0; Ambient = +40°C; Inner Conductor = 100°C (212°F); Sea Level; dry air; atmospheric pressure; no solar loading. Port 4 is the port which provides the reflected measurement (Return. e. In the ZS box, type a value of 75 Ω. =Γ2 = 10−RL/10 = Γ 2 = 10 − R L / 10. The VSWR/return loss calculator from Pasternack will find VSWR, return Loss, mismatch loss, and the reflection coefficient given any one of the listed input types. Cascaded Noise Figure calculator Chebyshev filter designer Coplanar GB waveguide calculator. This general RF calculator includes calculations of path loss, VSWR and wavelength as well as. Resistance Conversions. The magnitude has no units, since it is a ratio, and is also referred to as rho (ρ). For infinity:1 SWR the voltage and current are doubled, (at different places on the line), meaning you have to reduce power by four times for the same heating (some assumptions!). Jan 11, 2018 - Python Programmieren Lernen Pdf File. So a perfect match can be represented by the range 0. It is a Smith Chart based linear circuit simulation program that can be used via a website. 12:1, which is a. , the signal reflected back in a transmission line. Although the definitions of system cascaded parameters are pretty much standard throughout the industry, all of the formulas and assumptions used in RF Cascade Workbook are presented here in order to eliminate any ambiguity. The. RF Cascade Workbook for Excel. flectioncoefficientΓ,voltagestandingwaveratio(VSWR) and return loss (RL) and these quantities are interre-lated. NFsys = 9. The calculated value is MUCH worse. New for January 2021! This tool allows you to shift the frequency of an IF amplifier's S-parameters so you can cascade it with your RF chain in a receiver design. Return loss, also known as reflection loss, is a measure of the fraction of power that is not delivered by a source to a load. 0:1 --> S B = 2. PIM Calculator; Third order IP; Inductors. For example, if you wish to input "25000000", just type. Skin Depth Calculator. VNA Calibration Kit by Keysight Technologies ( 30 more products) Download Datasheet Request Quote. Advertisement. VSWR (Voltage Standing Wave Ratio) is the measure of how efficiently RF power is transmitted and is expressed as a ratio of the maximum to minimum. 5dBThis calculator converts between return loss (RL), voltage standing wave ration (VSWR), and reflection coefficient (Γ). Worksheet with more to be downloaded. I am using the specified max VSWR. 09 dB. 0:1, 2. This is ideal for applications requiring zero or low-frequency amplification. 001 watt then it. References. dl. 05:1 it calculates a VSWR of 1. RLC Combinations: Parallel. This can be achievedAs a further extension of this cascade of RC low pass filter sections add a third RC section to make a 3rd order filter by connecting R 3 and C 3 to your circuit as shown in figure 5. Resistance Conversions. It does not have null spots directly overhead or at other in-opportune locations like. In the old version, typing each time a new value. between the cascaded assembly and the load results in more power being re- flected back to the source. VSWR MIN = 2. Microstrip Patch Antenna Calculator Calculate dimensions and edge impedance for desired resonant frequency. is a VNA Calibration Kit with Frequency 110 to 170 GHz, Operating Temperature -20 to 30 Degree C, Return Loss 30 dB. - Return loss in dB. Enter the Noise Figure & Gain for each stage to calculate the Cascaded value Select Number of Stages Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Stage 7 Stage 8 Stage 9 Stage 10 NF(dB)VSWR Explained. Enter appropriate data See results in; dBm : dBw, Watts or microVolts. More details for V06CAL Series can be seen below. Calculate! Where do these calculations come from? Well, start with the formula for VSWR: If we invert this formula, we can calculate the reflection coefficient (, or the return loss. Basic VSWR calculations and formulas. 5 / 2. VSWR (input) : Return Loss in dB (output): Return loss calculation EXAMPLE : VSWR = 1. Python programmieren lernen pdf converter. It also shows the percentage of forward to reflected power. So, gamma. 具体的公式我不太知道. For Example WR-650 means a waveguide whose cross section width is 6500 mils. Do all your RF calculations using this application. 首页(放在最后了) 这个软件(工具集合)的不足之处. Formally, S11 is the negative of return loss and. VSWR and Return Loss Calculations. Enter the Return Loss (RL) in dB of each element in the RF chain. striker. This tool provides an estimate of the Return Loss of a cascade of two RF subsystems. The formula goes like this: gamma total = the square root of the sum of the squares of the individual gammas minus the product of the square of the individual gammas. 9 dB RL) S (min) = 1. Alternatively, Generate R1 and R2 for a wanted attenuation. • MTBF and MTTF Calculator • Power Unit Calculator • RF Phase Noise to Jitter Converter • ACPR Calculator • Cascaded IP3 Calculator • RF Amplifier PAE. Enter the sample rate of the ADC (Fsamp), Frequency (Fin) and optionally adjust the maximum harmonic to calculate (Nmax). 966 dB and have slightly underestimated the. To specify reference impedances for each frequency in this case, specify Z0 as a 3-D vector of length 1-by-1-by-K. Qorvo MatchCalc is a downloadable RF matching calculator designed to provide ideal component values for matching the impedance of a S1P or S2P file to a desired system or reference impedance. VSWR/Return loss converter Wavelength calculator Wilkinson splitter designer. VSWR is the ratio of the peak amplitude of a standing wave to the minimum amplitude of a standing wave, as seen in the following Figure: Figure 1. QFH antenna is one among various antennas used to capture images from low level non geosynchronous satellites. This RF/microwave system Cascade Analysis Calculator is an easy to use design analysis tool. They can be used to measure parameters like VSWR and Return loss, which only requires the. The Mini-Circuits RF / Microwave Calculator was developed by Mini-Circuits, an industry leader in the design, manufacture and distribution of RF and microwave. Cascaded calculations were carried out to determine the values at the system output, and then the equivalent input parameters were calculated. VSWR, Return Loss and Reflection Coefficient CalculatorsTherefore the VSWR of port 1 must equal that of port 4 and also port 3. Voltage standing wave ratio (VSWR) (pronounced "vizwar" [1] [2]) is the ratio of maximum to minimum voltage on a transmission line . e. Following calculator can be used to convert VSWR to corresponding return loss (RL). 99 = 1 −Γ2 = 1 − Γ 2. The lower noise figure number, the better. In his ATP he had the following formula to calculate the cascaded VSWR through the many switches to the front panel. These spurious signals can disturb the operational performance of the system in which the amplifier is used. This is for ideal conditions: stated as VSWR=1. Cascaded noise figure is an important figure of merit especially for receiver design. click on any item below to see example plots:Intermodulation calculators. Er:Dears, I would like to share this useful program from Kathrein Inc. Converts VSWR into dBm. Click here to learn about cascade analysis. Solution: Internally, this calculator first converts the given noise figure (in dB) inputs to normal values (i. Mismatch loss (ML) is the ratio of incident power to the difference between incident and reflected power: Figure 1. **Note: All of our calculators allow SI prefix input. Voltage Measured Along a Transmission Line. VSWR to Return Loss (dB) Calculator. 10. 1 Return loss in dB = 26. is a VNA Calibration Kit with Frequency 75 to 110 GHz, Operating Temperature -20 to 30 Degree C, Return Loss 35 dB. VSWR is defined as the ratio of the maximum to minimum voltage on a loss-less transmission line (expressed as 3. Upon arriving back at the source, part of the reflected wave is. But it does have a few entry boxes and drop-down menus that can take some time to familiarize yourself with. I am using the specified max VSWR. It also calculates the amplitude and phase error. The calculator converts between return-loss, VSWR, reflection coefficient, and mismatch loss. ashraferto. e. 5 GHz. In a perfectly matched system Z L =Z o, and there is no mismatch loss. M. This topic has moved to a separate page. It varies from 1 to (plus) infinity and is always positive.