Designing an effective base-transceiver-station (BTS) receiver for Long-Term Evolution (LTE) cellular applications includes meeting half-intermediate-frequency (half-IF) spurious requirements. To do this, it is necessary to understand the relationship between a mixer's second-order intercept point (IP2) and second-order response performance and then choose the appropriate RF mixer to meet the cascaded requirements. Mixer data sheets will provide second-order response information either in terms of IP2 performance or 2 x 2 spurious-rejection performance. By showing the relationship between those two parameters, it is possible to determine the overall half-IF spurious performance which can then be applied to the LTE BTS receiver design. The technique will be demonstrated for the MAX19997A, an active mixer used in an E-UTRA LTE1 receiver design.
In superheterodyne receiver circuits, mixers translate radio-frequency (RF) signals to lower intermediate-frequency (IF) signals. Known as downconversion, the process uses the difference frequency between the mixer's RF input signals and local-oscillator (LO) input signals for low-side injection (LO frequency < RF frequency), or the difference frequency between the mixer's LO and RF for high-side injection. This downconversion process can be described by the following equation:
fIF = fRF fLO = fRF + fLO
fIF = the IF at the mixer's output port;
fRF = any RF signal applied to the mixer's RF port; and
fLO = the LO signal applied to the mixer's LO port.
Ideally, the mixer's output signal amplitude and phase are proportional to its input signal's amplitude and phase; it is independent of the LO signal characteristics. Using this assumption, the amplitude response of the mixer is linear with respect to the RF input signal. It is also independent of the LO signal amplitude.
Mixer nonlinearities, however, produce undesired mixing products called spurious responses. The spurious responses are caused by undesired signals that reach the mixer's RF port and produce a response at the IF frequency. The signals reaching the RF input port need not fall into the desired RF band to be troublesome.
Many of these signals are sufficiently high in power level that the RF filters preceding the mixer do not provide sufficient attenuation to keep them from causing additional spurious responses. When these signals interfere with the desired IF frequency, the mixing mechanism is described by:
fIF = mfRF - nffLO = -mfRF + nffLO
Note that m and n are integer harmonics of both the RF and LO frequencies that mix to create numerous combinations of spurious products. Normally, the amplitude of these spurious components decreases as m or n increases.
Knowing the desired RF input-frequency range, frequency planning is used to carefully select the IF and resulting LO frequency. Accurate frequency planning is important because it minimizes mixing products that fall in the desired band which would, in turn, degrade the receiver performance. For wider bandwidth systems, avoiding spurious mixing products becomes significantly more difficult in frequency planning. Filters are used to reject out-of-band (OOB) RF signals that can cause unwanted in-band IF responses. IF filter selectivity following the mixer is specified to pass only the desired frequencies, thereby attenuating the spurious response signals ahead of the final detector that follows the mixer. Spurious responses that appear within the IF band will not be attenuated by the IF filter.
Many types of balanced mixers reject certain spurious responses where m or n is even. Ideal double-balanced mixers reject all responses where m or n (or both) is even. The IF, RF, and LO ports are mutually isolated in all double-balanced mixers to minimize LO leakage at the RF and IF ports and provide inherent RF-to-IF isolation. Double-balanced mixer design results in optimum linearity performance and reduces the associated filter attenuation requirements at each of the ports.
There is a particularly troublesome second-order spurious response called the half-IF (1/2 IF) spurious response, defined for the mixer indices of (m = 2, n = -2) for low-side LO injection and (m = -2, n = 2) for high-side LO injection (Fig. 1). For high-side injection, the input frequency that creates the half-IF spurious response is located above the desired RF frequency by an amount fIF/2 from the desired RF input frequency.
Consider an example where the desired RF signal is centered at 2510 MHz (E-UTRA uplink channel number 39790). When this RF signal is combined with an LO signal at 2860 MHz, the resulting IF is 350 M Hz. In this case, an undesired or blocking signal at 2685 MHz causes a half-IF spurious product at 350 MHz. For low-side injection, the input frequency that creates the half-IF spurious response is located above the desired LO frequency by an amount equal to fIF/2. Assume the following conditions for this example: an RF signal (fRF centered at 2510 MHz, an LO frequency (fLO) of 2860 MHz, and:
fIF = fLO - fRF =
2860 MHz - 2510 MHz = 350 MHz
The blocker frequency that causes an undesired spurious response can be calculated in the following way:
fHALF-IF = fRF + fIF/2 = 2685 MHz
This result can be verified by checking the math in the following way:
= 2(fRF + fIF) - 2(fRF + fIF/2)
= 2fRF + 2fIF - 2fRF - fIF = fIF
This results in the undesired IF spurious signal generated from the half-IF spurious frequency:
2 (2860 MHz) - 2 (2685 MHz) = 350 MHz
If not directly specified in a device's data sheet, the amount of rejection, called the 2 x 2 spurious response, can be predicted from the mixer's IP2 performance. Two assumptions are made: only the fundamental RF and LO frequencies are applied to the mixer ports, and the harmonic distortion is created in the mixer alone.
Image-reject filters used in the RF path immediately ahead of the mixer attenuate any undesired RF amplifier harmonics. The noise filter in the LO path attenuates harmonics caused by the LO injection source. High-level input signals create distortion or intermodulation products and can be quantified by calculating the IP, either at the input or output2 of the device or system. The input IP represents a hypothetical input amplitude at which the desired signal components and undesired components are equal in amplitude. For the case where the mixer's LO power is held constant, the order of the IP or distortion product is determined only by the RF multiplier and not by the LO multiplier. This is true because variations in the RF signal are the only concern. The order refers to how fast the amplitudes of the distortion products increase with a rise in input level. For example, because of the square-law relationship, the second-order intermodulation (IM) products will increase in amplitude by 2 dB when the input signal is raised by 1 dB.
The following discussion uses the MAX19997A3 downconversion mixer as the example. These values can be found in the AC Electrical Characteristics Table within the data sheet:
RF spurious power level (at 2685 MHz) = - dBm
LO level (at 2860 MHz) set = +0 dBm
Typical 2LO - 2RF spurious rejection is specified 64 dB below the RF carrier level in units of dBc; the -64 dBc value is referred to as the second-order intermodulation ratio (IMR2).
Calculate PSPUR = -5 dBm - 64 dBc = -69 dBm due to mixer performance.
This outstanding 2 x 2 performance for the MAX19997A results in the following equivalent IP2 performance at its input (IIP2):
IIP2 = 2 IMR2 + PSPUR = IMR2 + PRF
= 2 (64 dBc) + (-69 dBm) = 64 dBc + (-5 dBm)
= +59 dBm
Similarly, the MAX19985A4 900-MHz active mixer provides typical 2RF - 2LO spurious response equal to -71 dBc under similar conditions:
IIP2 = 2 IMR2 + PSPUR = IMR2 + PRF
= 2 (71 dBc) + (-76 dBm) = 71 dBc + (-5 dBm) = +66 dBm
Assuming that an E-UTRA LTE cellular system is colocated with a BTS of the same class, the resulting OOB CW blocker level is specified as +16 dBm (described in the 3GPP TS 36.104 V10.2.0 standards and illustrated in Fig. 2). For the LTE receiver, the equivalent IIP2 value required at the antenna terminal is +131 dBm due to the half-IF spurious signal. The following steps are used for this calculation:
Desired signal level = sensitivity power level (PSENSITIVITY) + 6 dB = -95.5 dBm.
For an LTE 5-MHz carrier, use SNR = -1.1 dB, which corresponds to the highest level of combined noise and spurious product, -96.6 dBm.
Determine the maximum allowable spurious product level = -98.9 dBm by subtracting thermal noise + noise figure in the desired bandwidth (in this example, subtract kTBF = -100.4 dBm).
Calculate the second-order intermodulation ratio, IMR2 = 115 dB.
Finally, calculate IIP2 = +131 dBm as shown in Fig. 2.
Refer to Fig. 3 for a simplified receiver front-end block diagram depicting stage gain, second-order IP, and half-IF selectivity for each stage through the first mixer.
The overall cascaded IIP2 performance is determined by a combination of stage gain, filter selectivity at the half-IF frequency, and mixer IIP2 (or 2 x 2) performance. Because the mixer dominates the cascaded IIP2 performance of the entire lineup, IIP2 values for the remaining stages are neglected in the following calculations. IIP2 is degraded (dB for dB) by the value of the power gain preceding the mixer in the lineup. In practice, RF selectivity at the half-IF frequency is added in front of the mixer to provide additional spurious rejection. The equivalent IP calculated at the antenna improves by twice the amount of the half-IF selectivity at the undesired blocking frequency in dB. This improvement occurs because the amplitude of the second-harmonic distortion component increases at a rate two times that of the desired on-channel signal. Using the calculated +59 dBm IIP2 value for the MAX19997A in an E-UTRA LTE 3GPP receiver design example, the cascaded IIP2 calculated at the antenna is:
IIP2Cascade = IIP2Mixer - Gain + 2 Selectivity = +131 dBm
IIP2Cascade = +59 dBm - (-2 + 13 + 13 - 2)dB + 2 (30 +17)dB = +131 dBm
The excellent 2LO - 2RF spurious performance of the MAX19997A is of significant value in a receiver design. It can ease the filter selectivity requirements to meet the receiver's half-IF spurious response (as shown in this example) or can provide margin-to-specification when using additional filter selectivity.
In conclusion, it has been shown how to determine the required half-IF spurious performance for an LTE receiver and convert the mixer's 2 x 2 spurious response value (IMR2) to its corresponding IIP2 value, and vice versa. Understanding this second-order relationship allows an RF engineer to determine the proper mixer performance level for the desired application.
The MAX19997A 2.5-GHz mixer and the MAX19985A 900-MHz mixer both provide superior 2 x 2 (IP2) performance, which eases filter requirements for the receiver's half-IF spurious performance. This makes these mixers ideal for high-performance wireless designs.
- 3GPP TS 36.104 V10.4.0, 3rd Generation Partnership Project; Technical Specification Group Radio Access Networks; Evolved Universal Terrestrial Radio Access (E_UTRA); Base Station (BS) radio transmission and reception (Release 10). See http://www.3gpp.org/ftp/Specs/html-info/25104.htm.
- The output intercept point is merely the input intercept point plus the gain (in dB) of the circuit or system under measurement.
- Maxim Integrated Products, Inc., data sheet for MAX19997A Dual SiGe, High-Linearity, 1800 to 2900 MHz downconversion mixer with LO buffer, available at www.maxim-ic.com/MAX19997A.
- Maxim Integrated Products, Inc., data sheet for MAX19985A 700 to 1000 MHz downconversion mixer with LO buffer/switch, available at www.maxim-ic.com.
For additional reading
- Lawrence E. Larson, RF and Microwave Circuit Design for Wireless Communications, Artech House, Norwood, MA, 1997.
- Peter Vizmuller, RF Design Guide Systems, Circuits, and Equations, Artech House, Norwood, MA, 1995
- Matt Loy, Editor, "Understanding and Enhancing Sensitivity in Receivers for Wireless Applications," Texas Instruments Technical Brief SWRA030, May 1999, at http://www.ti.com/lit/an/swra030/swra030.pdf (note: Texas Instruments is a registered trademark and registered service mark of Texas Instruments, Inc.).