AN IIP2 CALIBRATION TECHNIQUE FOR DIRECT CONVERSION RECEIVERS M. Hotti, J. Ryynanen, K. Kivekas1), K. Halonen Electronic Circuit Design Laboratory Helsinki University of Technology Otakaari 5 A, 02150 Espoo, Finland e-mail:
[email protected] 1) Nokia Research Center, Helsinki, Finland
ABSTRACT An improvement for a previously published IIP2 calibration method for a Gilbert cell type mixer is introduced. In the previous solution the IIP2 was degraded as a function of the baseband frequency when a mixer with RC load was used. This solution maintains a high IIP2 over the entire baseband channel in wideband systems. In order to implement an on-chip tuning engine the correct trimming code has to be detected. Two different solutions for the detection of the correct trimming code are discussed in this paper.
1. INTRODUCTION In direct conversion receivers, the second-order intermodulation distortion is a fundamental problem [1]. Since the RF signal is mixed directly to baseband, the second-order intermodulation term (IMD2) interferes the reception of the wanted signal. In a perfectly balanced Gilbert cell type mixer, the IMD2 is a common-mode signal and therefore does not present a problem. However, due to device mismatches, the balance between the negative and positive branch of the mixer is degraded and the second-order distortion becomes a problem. For example in WCDMA system, a high IIP2 is required and it should not degrade as a function of the baseband frequency. 2. PRESENT IIP2 CALIBRATION TECHNIQUES In the calibration scheme presented in [2] the IIP2 is improved by adjusting the input signal amplitude balance and LO signal duty cycle in a harmonic mixer. This is achieved by making slight changes in the DC operating
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points. The achieved improvement of the IIP2 of the mixer was approximately 10dB. In [3], a method called dynamic matching is presented. This concept is known as chopping where periodic random signal modulates the transconductance stages and the output of a Gilbert cell type mixer. The reported improvement of the IIP2 is at least 12dB for a BiCMOS mixer and 11dB for a CMOS mixer [3]. However, the method is quite complex and requires an additional clock signal, which can produce unwanted intermodulation products on the chip. The IIP2 cancellation in [4] introduces digitally controllable asymmetry in a Gilbert cell mixer. An AM modulated blocker is inserted into the receiver and the blocker induced change in the DC offset is nulled. The complete calibration scheme was not given in this paper. This method improved the IIP2 approximately 15dB. Several mismatch factors cause even order intermodulation distortion in a Gilbert cell type mixer. A simplified behavioral model of a transconductance mixer is presented in [5], where the IIP2 for a double balanced mixer is calculated,
IIP 2 =
×
2
πη nomα 2 '
4 , (2∆η (∆g m + ∆ARF ) + ∆R(1 + ∆g m )(1 + ∆ARF ))
(1)
where η is the duty cycle, α’2 is the second order nonlinearity factor, gm is the transconductance of the input device, ∆ARF is the amplitude imbalance in the RF signal, and ∆R the resistor imbalance. It can be noticed from (1) that IIP2 can be trimmed by controlling the load resistor of the mixer. A simple method presented in [6] applies controllable resistor matrix at the output of a Gilbert cell type mixer.
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,6&$6
However, the drawback of this technique is the deterioration of the IIP2 as a function of the baseband frequency [6]. The reason for this phenomenon is the change in the frequency of the RC pole at the mixers output. 3. AN IMPROVED IIP2 CALIBRATION METHOD
To prevent the IIP2 deterioration as a function of the baseband frequency it is possible to implement tuning capacitors as well as tuning resistors at the mixer output. An example of this is shown in Fig. 1. The correct trimming capacitor CTRIM can be calculated from æR × C NOM CTRIM = çç NOM RTRIM è
ö ÷÷ , ø
(2)
Table 1. The performance of the mixer at 2GHz. Parameter: Value: Gain 9.3dB NFDSB 11.9dB IIP3 7.8dBm ICP -8.0dBm Current cons. 4.4mA In Fig. 2, the improvement to the nominal, resistortuned, and RC-tuned IIP2 are presented as a function of the baseband frequency. It can be noticed that the resistor tuning (R-trimmed) causes a significant dip in the IF response, but it can be compensated with the capacitor tuning (RC-trimmed). At high frequencies the RC pole starts to filter out the IMD2 term. Simulations were made with 5° phase imbalance in the differential LO signal. The RC pole frequency was located at 1.92MHz. IIP2 Improvement (dB)
where RNOM and CNOM are the nominal load resistance and capacitance, respectively. RTRIM is the trimming resistance.
equivalent to (n+1)-bit resolution in one branch. The simulations in this chapter are made for a mixer with single input, presented in Fig. 1, which has tuning on the positive load only. The performance table of the mixer is presented in Table 1.
25 20
RC-trimmed
15 10 5 0 0.1
R-trimmed
Nominal 1 Frequency (MHz)
Fig. 2. IIP2 improvement as a function of the baseband frequency. The improvement of the IIP2 depends on the accuracy of the tuning and in Fig. 3 an example of this is presented. The theoretical IIP2 improvement is marked with solid line and the 5-bit resistor tuning with dots. The tuning range is –10%...+10% of the nominal resistor. It can be noticed that 5-bit resolution is adequate to achieve +30dBm improvement to the IIP2 in this case.
Fig. 1. Mixer with RC-calibration in one branch. This tuning technique can be used in a single-input or differential input mixer. The tuning matrix can be implemented in both mixer loads or just in one load. In practice, it is possible to achieve adequate resolution with both ways. The n-bit resolution in both branches is
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4. DETECTION OF THE CORRECT TUNING CODE
IIP2 Improvement (dB)
40 35 30
For an on-chip IIP2 tuning engine the correct tuning code has to be detected. This can be done, for example, by inserting two test tones at the input of the receiver and minimizing the second order intermodulation term. However, this method requires two test tones and amplification for the detection of the weak IMD2 term. For example, if the gain of the RF front-end is 30dB, the power level of the test signals is –50dBm and the trimmed IIP2 of the front-end is +45dBm, the IMD2 term at the mixer output becomes hard to detect as shown in,
25 20 15 10 5 0 -10
-5
0 RTRIM (%)
5
10
IMD 2 = 2 PIN − IIP 2 + G FRONT − END = −115dBm .
Fig. 3. IIP2 improvement as a function of tuning. Due to the random nature of the IIP2 the correct trimming code can be found at the extreme limit of the tuning range. Thus, the baseband should be able to compensate the DC offset caused by this code. In addition, the large imbalance can cause LO noise leakage to the mixer output. The DC-offset problem can be solved with AC-coupled tuning resistors connected at the mixer output. This technique is presented in Fig 4.
(3)
Another method to detect the correct trimming code is to measure the DC offset at mixer output without a signal and then insert a test signal into the input of the receiver and measure the DC offset. In order to have a proper detection of the correct trimming code, the static DC offset due to the LO self mixing and device mismatch cannot change between these tests. The principle of this method is presented in Fig. 5.
Fig. 5. DC offset change minimization. The second order distortion produces a static DC offset to the output of the mixer as well as the IMD2 term. The IMD2 and static DC offset are,
Fig. 4. Mixer with AC coupled load. In this case, the load tuning does not affect the DC level at the mixer output, because there is no DC current through the trimming resistors.
IMD 2 = A1 A2α 2 [cos(ω1 + ω 2 )t + cos(ω1 − ω 2 )t ] ,
(4)
æA2 A 2ö DC STATIC = α 2 ç 1 + 2 ÷ , ç 2 2 ÷ø è
(5)
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where the A1 and A2 are the amplitudes of the input signals, α2 is the second order nonlinearity factor, ω1 and ω2 are the input signal frequencies and t is time. Therefore, by minimizing the change in the DC offset, it is possible to detect the correct trimming code. This method requires only one test tone and is easier to implement because only the DC offset has to be measured. However, according to simulations, the change in the DC offset is 5.1uV when ∆R=1% and the level of the test signal is –20dBm. This change has to be amplified which can be achieved by utilizing the baseband. For example, if the DC gain of the baseband is 80dB, the change in the DC offset would be 51mV. As it was previously shown, an infinite IIP2 cannot be achieved with a finite tuning resolution. Therefore, the change in the DC offset cannot be nulled. Thus, by minimizing the change in the DC offset the IIP2 is maximized. The used test signal could be from the transmitter, which usually produces the strongest interfering signal.
[4] R. Magoon, A. Molnar, J. Zachan, G. Hatcher, W. Rhee, “A Single-Chip Quad-Band (850/900/1800/1900 MHz) Direct Conversion GSM/GPRS RF Transceiver with Integrated VCOs and Fractional-N Synthesizer,” IEEE Journal of Solid-State Circuits, vol 37, pp. 1710-1720, Dec. 2002. [5] K. Kivekas, A. Parssinen, K. Halonen, “Characterization of IIP2 and DC-Offsets in Transconductance Mixers,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing,, vol 48, pp. 1028-1038, Nov. 2002. [6] K. Kivekas, A. Parssinen, J. Ryynanen, J, Jussila, K. Halonen, “Calibration Techniques af Active BiCMOS Mixers,” IEEE Journal of Solid-State Circuits, vol 37, pp. 766-769, June 2002.
5. CONCLUSIONS
In this paper, an improvement for a previously published IIP2 calibration technique is described and analyzed. In the previous solution a constant improved IIP2 was not maintained over the entire baseband channel. The technique presented in this paper solves this problem. Two possibilities for the detection of the correct trimming code for an IIP2 tuning engine were discussed. 6. ACKNOWLEDGEMENTS
The authors would like to thank Mr. Jouni Kaukovuori, Mr. Arto Malinen, and Dr. Jarkko Jussila for their contributions. The simulations were performed with APLAC circuit simulator. This work was supported by Nokia Networks and Finnish National Technology Agency. 7. REFERENCES [1] A. A. Abidi, “Direct-Conversion Radio Transceivers for Digital Communications,” IEEE Journal of Solid-State Circuits, vol 30, pp. 1399-1410, Dec. 1995. [2] T. Yamaji, H. Tanimoto, H. Kokatsu, “An I/Q Active Balanced Harmonic Mixer with IM2 Cancelers and a 45° Phase Shifter,” IEEE Journal of Solid-State Circuits, vol 33, pp. 22402246, Dec. 1998. [3] E. Bautista, B. Bastani, J. Heck, “A High IIP2 Downconversion Mixer Using Dynamic Matching,” IEEE Journal of Solid-State Circuits, vol 35, pp. 1934-1941, Dec. 2000.
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