The previous article in this series presented a cascade analysis of the noise level, noise floor, bandwidth, and signal-to-noise ratio of a simple RF front-end with a single gain stage. Based on the same concepts, this application note guides designers to calculate the parameters of a more complex signal chain that includes multiple nonlinear components such as mixers and IF amplifiers. The six-component front-end shown here can be used for the 26GHz 5G new radio band (FR2).
5G in Australia: Background
The 24.25-27.5 GHz frequency band is referred to as the “wide 26 GHz band,” or “5G band n258.” The Australian Communications and Media Authority (ACMA) has stated that it “recognizes that the 26 GHz band of wideband millimeter wave (mmWave) is at the forefront of the delivery of millimeter wave 5G wireless broadband services globally.”1 As a result, most of the spectrum, primarily in the 25.1-27.5 GHz band, was auctioned to telecommunications operators in April 2021.1 The 24.25-24.7 GHz band was designated as indoor use, and the 24.7-25.1 GHz band was designated as indoor/outdoor use.1 The RF front-end objective of this application note focuses on the lower part of the Australian 5G frequency range, between 24.25-25.1 GHz.
N258 Band front end chain
Figure 1 shows an RF front-end capable of covering the 24.25-25.1 GHz portion of the 5G n258 frequency band. The design includes a powerful preselector suitable for 5G and a high-performance MMIC LNA that is even more cost-effective. A 3 dB attenuator mitigates any VSWR degradation that may occur between the LNA and the mixer. The mixer itself is capable of LO/RF operation from 10-40 GHz, providing ample coverage of the band of interest. In this application, a 20 GHz LO is operated at +15 dBm, and the IF band is in the range of 4.25-5.1 GHz.
The IF filter is a small, ultra-high attenuation LTCC filter with a 3dB bandwidth of approximately 1200MHz.
The IF amplifier is a high gain, low noise MMIC that easily covers the 4.25 to 5.1GHz IF operating band.
The characteristics of each of the six components in the block diagram are shown below.
- Preselector (ZVBP-25875-K+ cavity filter): 24.25-27.5 GHz bandwidth, 1.72 dB insertion loss at 24.25 GHz
- LNA (PMA3-34GLN+): 21.65 dB gain at 25 GHz, 1.59 dB NF
- Attenuator (QAT-3+): 3.15 dB insertion loss at 25 GHz
- Mixer (MDB-44H+): 10.4 dB conversion loss. At RF = 25 GHz, LO = 20 GHz, and IF = 5 GHz
- IF Filter (BFHK-4951+): 2.65dB insertion loss (5.1 GHz), 3dB bandwidth approximately 4.1 – 5.3 GHz
- IF Amplifier (PMA3-83LNW+): 20.56dB gain and 1.59dB NF at 5GHz
Noise and SNR
Noise and SNR are generally easier to work with than NF, so we will focus on them first and determine the thermal noise floor (PThermal):
P_{\text{Thermal}} = kT_0 BWhere,
k = 1.38 \times 10^{-23} \text{ J/K (Boltzmann's constant)}, \quad T_0 = 290\text{ K nom. per IEEE}, \quad B = \text{Bandwidth (1 Hz)}\begin{aligned} P_{\text{Thermal}} &= (1.38 \times 10^{-23} \text{ J/}\cancel{\text{K}})(290\cancel{\text{K}})(1\text{ Hz}) = 4 \times 10^{-21}\text{ W} = 4 \times 10^{-18}\text{ mW} \\ &\Rightarrow 10\log(4 \times 10^{-18}\text{ mW}) = -174\text{ dBm in a 1 Hz BW, or } -174\text{ dBm/Hz} \end{aligned}Next, determine the noise floor of each stage of the system in a 1Hz bandwidth as it converts from RF input to IF output. This is actually very easy:
P_{\text{Noise}}\text{ (dBm/Hz)} = P_{\text{Noise(prev)}}\text{ (dBm/Hz)} + \text{Gain}_c + \text{NF}_cWhere PNoise(prev) = PNoise of the previous stage, Gainc = cascaded gain (dB), NFc = cascaded NF (dB)
(Note: Gainc and NFc include the current stage)
As a result, after the LNA we have:
P_{\text{Noise}} = -174.00\text{ dBm/Hz} + 19.93\text{ dB} + 3.31\text{ dB} = -150.76\text{ dBm/Hz}The calculated results for each stage are shown in the table section of Figure 2.
PNoise (dBm/BW), shown in Figure 2, is a way of expressing the noise floor in a system with a bandwidth other than 1Hz.
This shows the increase in noise power as the system bandwidth increases. Out of the box, the preselector limits the noise bandwidth to 3.25GHz, which corresponds to a noise floor of -78.88dBm. Wait a sec. What happened?
The thermal noise floor (PThermal), referenced exactly to 1Hz, was adjusted for a 3.25GHz system as follows:
\begin{aligned} P_{\text{Noise}}\text{ (dBm/BW)} &= -174\text{ dBm/Hz} + 10\log(\text{BW (Hz)}) + \text{Gain}_c\text{ dB} + \text{NF}_c \\ &= -174 + 10\log(3.25 \times 10^{9}\text{ Hz}) - 1.72 + 1.72 \\ &= -78.88\text{ dBm} \end{aligned}Note: This article uses the 3 dB bandwidth of the preselector (3.25 GHz) and IF filter (1.2 GHz) as an approximation of the equivalent noise bandwidth (ENB). Click here for details.
Strictly speaking, the value used as the noise bandwidth in the calculation above is the filter’s 3 dB bandwidth, but the equivalent noise bandwidth (ENB) Bn should be used for an exact noise power calculation:
B_n = \frac{1}{|H(f_0)|^2} \int_0^{\infty} |H(f)|^2 \, dfIn general, the ENB is not equal to the 3 dB bandwidth. For example, for a single-pole filter:
B_n = \frac{\pi}{2} \times BW_{\text{3dB}}However, the preselector (ZVBP-25875-K+) and IF filter (BFHK-4951+) used in this article are cavity and LTCC bandpass filters, respectively, with steep skirt characteristics, and their passband shapes closely approximate a brick-wall response, making the use of the 3 dB bandwidth as an approximation of ENB entirely reasonable.
The same result can be obtained by considering the relationship below. The noise floor of 1Hz BW is simply scaled to the system bandwidth.
P_{\text{Noise}}\text{ (dBm/BW)} = P_{\text{Noise}}\text{ (dBm/Hz)} + 10\log(\text{BW (Hz)})In the first equation for the system bandwidth noise floor, note that the 1.72dB insertion loss of the preselector ZVBP-25875-K+ cancels the NF. This is just one passive component in the system at this point. Since we know that the preselector insertion loss cannot attenuate the thermal noise floor (PThermal) below the -174dBm/Hz level, it is natural that the insertion loss and NF fall out of the equation.
If we define the input signal level at which the IF amplifier will not compress as -10dBm, we can easily find the signal-to-noise ratio (SNR) after the preselector in dB:
\begin{aligned} \text{SNR (dB)} &= 10\log\!\left(\frac{\text{Signal (mW)}}{P_{\text{Noise}}\text{ (mW)}}\right) \\ &= 10\log(\text{Signal (mW)}) - 10\log(P_{\text{Noise}}\text{ (mW)}) \\ &= \text{Signal (dBm)} - P_{\text{Noise}}\text{ (dBm)} \\ &= -11.72\text{ dBm} - (-78.88\text{ dBm}) = 67.16\text{ dB} \end{aligned}This SNR is shown in the table section of Figure 2 under “Post Stage 1” for the preselector. Note that the RF input signal level of -10 dBm is attenuated by the preselector insertion loss (1.72 dB) in the calculations, and the system bandwidth determines PNoise. In the later stages, the signal simply increases or decreases due to the gain, but the noise power (PNoise) is affected by several factors.The gain/loss and noise figure (NF) of components such as amplifiers directly affect the noise floor. In addition, changing the system bandwidth definitely affects the noise floor of the system, just as the preselector bandwidth of 3.25GHz resulted in a much larger PNoise level, which is very different from the PNoise of a 1Hz bandwidth.
There is one calculation anomaly that occurs very often when the receiver front end includes a conversion to an IF frequency. The preselector sets the system bandwidth to 3.25 GHz (24.25 – 27.5 GHz) and it remains there until the IF filter makes a significant change to the system bandwidth. The BFHK-4951+ limits the system bandwidth to 1.2 GHz (4.1 to 5.3 GHz). The effect of this bandwidth change can be seen in the PNoise (dBm/BW) section that occurs after “Post Stage 5”. If the bandwidth is not changed, the previous formula becomes:
\begin{aligned} P_{\text{Noise}}\text{ (dBm/BW)} &= P_{\text{Noise}}\text{ (dBm/Hz)} + 10\log(\text{BW (Hz)}) \\ &= -166.19\text{ dBm/Hz} + 10\log(3.25 \times 10^{9}\text{ Hz}) \\ &= -71.07\text{ dBm} \quad (3.25\text{ GHz bandwidth}) \end{aligned}However, to get accurate results it is important to take into account that the IF filter narrows the system bandwidth from 3.25 GHz to 1.2 GHz:
\begin{aligned} P_{\text{Noise}}\text{ (dBm/BW)} &= P_{\text{Noise}}\text{ (dBm/Hz)} + 10\log(\text{BW (Hz)}) \\ &= -166.19\text{ dBm/Hz} + 10\log(1.2 \times 10^{9}\text{ Hz}) \\ &= -75.40\text{ dBm} \quad (1.2\text{ GHz bandwidth}) \end{aligned}Note that a reduction in system bandwidth naturally leads to a reduction in PNoise.
Cascaded Gain and Noise Figure
The gain and noise figure of the first stage are simple, exactly the insertion loss of the preselector ZVBP-25875-K+ (1.72dB), the gain is a negative value and the NF is a positive value.
What happens when you cascade a preselector with an LNA, an attenuator, a mixer, an IF filter, and an IF amplifier in series? Looking at the parameters following each stage in the table in Figure 2, the cumulative gain after each stage is determined by simply adding it to the cumulative gain up to the previous stage. That is:
G_{\text{cum}(n)}\text{ (dB)} = G_{\text{cum}(n-1)} + G_nFor the entire 6 component cascade:
\begin{aligned} G_{\text{Tot}}\text{ (dB)} &= G_1 + G_2 + G_3 + G_4 + G_5 + G_6 \\ &= -1.72\text{ dB} + 21.65\text{ dB} - 3.15\text{ dB} - 10.40\text{ dB} - 2.65\text{ dB} + 20.56\text{ dB} \\ &= 24.29\text{ dB} \end{aligned}Noise figure becomes a very complicated parameter when components are cascaded across the front end. The noise figure (NF) in dB must be converted to a noise factor (F) and calculated using the Friis formula2.
For the first two stages (preselector/amplifier), the noise figures (NF) of each stage can simply be added in dB (1.72dB + 1.59dB = 3.31dB), the result of which is shown in Figure 2 in the “Post Stage 2” column. Once gain is introduced and given the elements following it in the signal chain, the Friis formula is used as shown below:
F_{\text{Total}} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \frac{F_4 - 1}{G_1 G_2 G_3} + \frac{F_5 - 1}{G_1 G_2 G_3 G_4} + \frac{F_6 - 1}{G_1 G_2 G_3 G_4 G_5}To convert to noise figure:
\text{NF}_{\text{Total}} = 10\log(F_{\text{Total}})Alternatively, the Friis formula can be used once per stage to display the cumulative NF for each component added to the system.
The noise factor is given by the formula below:
F = 10^{(\text{NF}/10)}Accordingly:
\begin{aligned} F_1 &= 10^{(1.72\text{ dB}/10)} = 1.49 \\ F_2 &= 10^{(1.59\text{ dB}/10)} = 1.44 \\ F_3 &= 10^{(3.15\text{ dB}/10)} = 2.07 \\ F_4 &= \ldots \end{aligned}Gain (Gn) is the cascaded gain of the element related to Fn+1 up to the point where it is connected to the system. The gain must be a linear ratio (e.g. G1 = 10(-1.72 dB/10) = 0.67).
Signal to Noise Ratio (SNR)
The SNR can be determined by simply subtracting two values in dBm: the signal level and the noise level over the system bandwidth, shown in Figure 2 as dBm/BW. The SNR can be determined at any stage by the following calculation:
\text{SNR} = \text{Signal level (dBm)} - P_{\text{Noise}}\text{ (dBm/BW)}Cascade Effect
This article briefly describes the cascade analysis of noise and signal-to-noise ratio of a six-component RF front-end designed for the 5G n258 band from 24.25 to 25.1 GHz. It then presents the step-by-step calculation of the thermal noise floor and noise floor at a given system bandwidth, as well as the signal-to-noise ratio (SNR). The Friis formula was used to calculate the cascade noise figure. The noise level calculations (including accounting for the effect of changing the system bandwidth) and SNR calculations were simplified by starting the signal level at -10 dBm and were done using the cascaded gain and NF values. Future articles in this series will discuss additional cascaded parameters such as linearity in terms of P1dB and IP3 for similar front-end designs.
Products Used in This App Note
References
- Australian Communications and Media Authority (ACMA), Australian Government, Auction Overview – 26 GHz Band (2021), Last updated: 3 March 2022.
- H.T. Friis, “Noise Figures of Radio Receivers,” Proc. IRE, vol. 32, no. 7, pp. 419–422, July 1944.