A Charge-Sharing Bandpass Filter Topology with Boosted Q-Factor in 40-NM CMOS
Summary (2 min read)
Introduction
- Nevertheless, complex strategies were sometimes required to overcome the typical issues of 2nd order non-linearity, flicker noise and DC offsets [1]–[3].
- The introduction of N-path filters in the RF front-end led the way to the start of this new revived interest in super-heterodyne receivers [4].
- The main drawback presented by this solution are the filter replicas at the sampling rate as a consequence of the discrete-time (DT) nature of the filter, which are then folded back to the band of interest.
- Its main advantages over the traditional CS-BPF approach are discussed, and the small noise impact of the circuit modification is carefully analysed.
II. CHARGE-SHARING BANDPASS FILTER
- The basic charge-sharing bandpass filter (CS-BPF) is synthesized from the 4th-order Infinite Impulse Response (IIR) lowpass filter (LPF) [7].
- To include these variations, a more general CS-BPF transfer function is given by (2).
- In comparison to the 4/4-phase CS-BPF, the 8/8- phase CS-BPF has a better filtering characteristic but the attenuation far from the central frequency is limited.
III. MODIFIED CHARGE-SHARING BANDPASS FILTER
- Even though both methodologies are very effective to increase the Q-factor of the CS-BPF, they also increase the overall number of switches, the number of clock buffers, and consequently the power consumption.
- Hence, each of the clock generation circuits is going to consume 2x more power.
- Secondly, as the order of the CS-BPF increases, a secondary peak appears.
- Based on these points, the authors conclude that increasing the order of the filter beyond two (e.g., 4/8-phase BPF) is hardly worth the cost of complexity and power consumption.
- Fig. 4 shows the schematic of a 4/8 CS-BPF modified using this negative impedance.
B. Noise analysis of the modified charge-sharing bandpass filter
- Based on the noise analysis of the 4/4-phase CS-BPF presented in [7], the noise contribution of the modified 4/8-phase CS-BPF is presented hereafter.
- Hence, after taking the folding into consideration, the sampled noise PSD of the switch and the inverter are given by (9) and (10), respectively [13].
- The purpose of this analysis is to compare the noise of the 4/8-phase CS-BPF with and without the addition of the negative impedance.
- The noise sources are uncorrelated, so superposition can be used to compute the contribution of each source to the output noise.
- Fig. 7 shows the output noise of the filter with and without the negative impedance.
IV. CIRCUIT IMPLEMENTATION
- The modified 4/8-phase CS-BPF was implemented and measured as the second filtering stage of a complete receiver presented in fig. 8 [6].
- The RF front-end is composed of wideband LNTA, 25% duty-cycle sampling mixer, 4/4 full-rate CS-BPF which operates at the mixer sampling rate, and clock generation circuits.
- The second stage is composed of a basic ”inverter-like” transconductor (Gm-cell) stage detailed in fig.
- The Gm-cell gives a gain of 12.8 dB when combined with the filter input resistance.
- The eight 12.5% duty-cycle clock phases required by the filter are generated by the frequency divider-by-4 (fig. 10(a)).
V. RESULTS
- The DT filter was implemented in silicon as part of the receiver designed and fabricated in TSMC 40-nm CMOS (fig. 11) [6].
- The filter, the Gm-cell and the 8-phase clock generation circuit jointly occupy a slicon area of 0.24 x 0.28 mm2.
- According to (3), the resolution of the capacitor banks allow for center frequency programming in the range of 20 MHz to 60 MHz, which creates a variable passband characteristic due to the constant quality-factor presented by their filter design.
- As expected by the noise analysis, noise figure is not strongly impacted by the modification (fig. 13(b)).
VI. CONCLUSION
- This paper presented a detailed analysis of a newly modified charge-sharing bandpass filter.
- The discrete-time filter is fully-programmable, which allows for both intermediate frequency and passband adjustments.
- This flexibility makes this technique a good candidate for narrowband and wideband RF transceiver applications.
- The charge-sharing bandpass filter topology is modified using cross-connected transconductors at the filter inputs which enables higher selectivity without increasing complexity, noise and power consumption.
- The filter is implemented in 40-nm bulk CMOS and it occupies an area of 0.24 x 0.28 mm2, considering the transconductor amplifier, and the clock generation circuit area altogether.
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Frequently Asked Questions (18)
Q2. What is the effect of the negative impedance on the noise of the filter?
Since the negative impedance enhances the gain of the filter, a slight reduction of the noise is observed, and a small impact in the overall RX noise figure is expected.
Q3. What is the size of the filter?
The filter is implemented in 40-nm bulk CMOS and it occupies an area of 0.24 x 0.28 mm2, considering the transconductor amplifier, and the clock generation circuit area altogether.
Q4. What is the noise transfer function of vn1 to each output?
By converting (11) - (14) from the time-domain to the z-domain, the noise transfer function of vn1 to each output isH1 =( 1− az−1 )7 bz−1 − ( 1− az−1 )6 b2z−1 +A1− (1− az−1)8 + b8z−8 +B1 , (15)H2 =( 1− az−1 )5 b3z−3 − ( 1− az−1 )4 b4z−3 +A2− (1− az−1)8 + b8z−8 +B1 , (16)H3 =( 1− az−1 )3 b5z−5 − ( 1− az−1 )2 b6z−5 +A3− (1− az−1)8 + b8z−8 +B1 , (17)H4 =( 1− az−1 ) b7z−7 − b8z−7 +A4− (1− az−1)8 + b8z−8 +B1 , (18)where H1, H2, H3, and H4 are the noise TFs to vout,0◦ , vout,90◦ , vout,180◦ , and vout,270◦ , respectively.
Q5. What is the basic charge-sharing bandpass filter?
In this circuit, an input charge packet is stored in a history capacitor (CH ), and on phase φ1, partially transferred to a previously discharged rotating capacitor (CR), acting as a lossy component.
Q6. What is the input resistance of the filter?
4. The feedback gain β is implemented as Gm x Rin, where Gm is the inverter transcondutance, and Rin is the input resistance of the filter, Rin ≈ 1/fsCR.
Q7. What is the purpose of this analysis?
The purpose of this analysis is to compare the noise of the 4/8-phase CS-BPF with and without the addition of the negative impedance.
Q8. How many mW of gain is the Gm-cell?
The measured power consumption of the Gm-cell with 12.8 dB of gain and the clock generation circuits operating at 500 MHz are 2.7 mW and 5.35 mW respectively, from a 0.9V power supply.
Q9. What is the name of the generic CS-BPF?
In [10], a generic CS-BPF has been presented and named as M/N-phase CSBPF, where M is the number of inputs and N the number of phases.
Q10. What is the transfer function of the 8/8-phase CS-BPF?
In comparison to the 4/4-phase CS-BPF, the 8/8- phase CS-BPF has a better filtering characteristic but the attenuation far from the central frequency is limited.
Q11. What is the Q-factor of the CS-BPF?
Another possibility to enhance the Q-factor is by adding a pair of cross-connected transconductors at both the in-phase (I) and quadrature (Q) inputs of the filter.
Q12. what is the noise TF of the 4/8-phase CS-BPF?
the terms A1, A2, A3, A4, and B1 are introduced by the negative impedance and presented below:A1 = [ −2 ( 1− az−1 ) + b ] [( 1− az−1 )4 b3β2z−1+ ( 1− az−1 ) b6βz−5 ] + ( 1− az−1 )3 b5β4z−1, (19)A2 = − ( 1− az−1 )3 b5β2z−3− ( 1− az−1 )2 b6β2z−3 − b8βz−7, (20)A3 = − ( 1− az−1 )5 b3βz−1 + ( 1− az−1 )3 b5β3z−1+ ( 1− az−1 ) b7β2z−5, (21)A4 = − [ − ( 1− az−1 )2 − 2 (1− az−1) b− β2b2]( 1− az−1 )2 βb4z−3, (22)B1 = 2 ( 1− az−1 )6 b2β2 − ( 1− az−1 )4 b4β4+ 4 ( 1− az−1 )3 b5βz−4. (23)Hence, if these terms are considered zero, the authors have the noise TF of the original 4/8-phase CS-BPF.
Q13. What is the transfer function of a CS-BPF?
Regardless of the number of inputs and the order, the central frequency of the CS-BPF is solely controlled by the ratio of the capacitors CH and CR.
Q14. How can the authors increase the order of the IIR LPF?
The order of the IIR LPF can be easily increased by adding more CH capacitors to share the charge stored in CR during subsequent phases, φ1, φ2 and so forth [8].
Q15. What is the transfer function of the two Q-factor enhancing alternatives?
H(z) = k [ (1− a) z−1 ]N/M−1 (1− az−1)N/M − ej 2πM [(1− a) z−1]N/M . (2)Based on (2), the transfer functions of two Q-factor enhancing alternatives are presented in fig.
Q16. What is the noise of the other inputs and outputs?
The time-domain noise equations of the other three inputs and outputs arevout,i[n] = avout,i[n− 1] + bvin,i[n− 1], (13)vin,i[n] = avin,i[n− 1] + bvout,i−90◦ [n− 1] + βbvin,i−180◦ [n], (14)where i ∈ {90◦, 180◦, 270◦}.
Q17. What is the noise of the first output and input at t = nTs?
The time-domain noise of the first output and input at t = nTs is given byvout,0◦ [n] = avout,0◦ [n− 1] + bvin,0◦ [n− 1]− bvn1[n− 1], (11)vin,0◦ [n] = avin,0◦ [n− 1] + bvout,270◦ [n− 1] + βbvin,180◦ [n] + bvn1[n], (12)where b = 1 − a, and vn1 = √ V 2n1.
Q18. How many switches are there in the CS-BPF?
For instance, considering only the number of switches, the power consumption of the 4/8-phase BPF is 4x higher than the 4/4-phase BPF.