Sampling IF filters Fortify Bluetooth Designs

The sampling intermediate-frequency (IF) filter is a high-performance digital device that can bring increased yield to integrated Bluetooth receiver designs.

Bluetooth system architects strive to reduce cost, component count, and power consumption while maintaining high production yields for both chips and modules. Traditionally, the first three requirements are met by integrating off-chip components. However, a high level of analog integration adversely affects chip yield. Because of market demands for reduced cost and low component counts, Bluetooth is a prime example of a system-on-a-chip (SoC) technology reaching higher levels of integration. As an alternative low-power approach, it is possible to integrate intermediate-frequency (IF) filters in a Bluetooth receiver (Rx) for increased yield over other techniques.

Two well-known filter technologies have been used for integrating Bluetooth IF filters on chip: the switched-capacitor (SC) filter and the transconductor-capacitor (gm-C) filter. SC filters are constructed by substituting the resistors in an active RC filter with switches and capacitors. These SC filters have very precisely defined bandpass characteristics because the time constants associated with the frequency response depend only on the capacitor ratios and the clock frequency. A serious drawback with using SC filters in an IF stage is the danger of aliasing interfering signals. Since the operational amplifiers (opamps) used in SC filters must have greater bandwidth than the signal they are processing, power consumption tends to be high. The noise problem can be solved by using larger capacitors, but these consume more power. These noise and aliasing issues are further compounded in systems requiring low-power, low-clock-rate operation. As an example,1 the signal-to-noise ratio (SNR) of one SC filter was 31 dB, which is the equivalent of 14 nV/(Hz)0.5 and a current consumption of 10 mA.

A gm-C filter is constructed by replacing the inductor (L) in an LC filter with a capacitor and a gyrator made from a transconductance amplifier. Typically, gm-C filters provide lower noise and lower-power operation than SC filters but suffer in two problem areas where SC filters perform better. There is typically a trade-off where gm-C filters require more power to provide adequate linearity. Since the time constants in a gm-C filter depend on two independent process variables (gm and C), they tend to have poorly controlled passband frequency response characteristics unless a process calibration loop is included. This can adversely effect the chip yield and result in additional wafer runs for a given chip. The image-band rejection (IBR) is sensitive to the bias current and other filter parameters.2 Depending on the software models used for simulating the transistors in the filter, simulations could indicate a stable filter if the models are too simple. Once fabricated, the filters could still be unstable. As an example of this technology (see ref. 3), consider a gm-C filter with input noise of 250 mV, which is the equivalent of 10 nV/(Hz)0.5 and current consumption of 6.2 mA.

The new "sampling IF filter" technology, combines the low-power, low-noise properties of a gm-C filter with the precisely controlled passband and process independence of a SC filter. This single unit incorporates an automatic-gain-control (AGC) stage, anti-aliasing filter, channel-selection filter, and sampler. Sampling IF filters can also replace off-chip surface-acoustic-wave (SAW) filters. This method substantially reduces both speed and resolution requirements specified for an analog-to-digital converter (ADC) because the channel-selection filtering is performed before the sampler and ADC. This saves power and allows the use of a simpler ADC.

Figure 1 shows a simplified circuit diagram of a sampling IF filter. Typically, this approach employs differential circuitry, although the diagram of Fig. 1 shows a single-ended version for simplicity. In a differential circuit, the −1 block can be implemented by crossing a pair of wires to invert the polarity of the current. To build finite-impulse-response (FIR) filters with an arbitrary sequence of tap coefficients whose values are 1, −1, or 0, the corresponding P+, P-, or P0, respectively, are set to be high at any one time. These quantized tap coefficients can be derived from an ideal FIR impulse response by delta-sigma (DS) quantization (ref. 4). Since the continuous-time input Vin is integrated continuously over the sample intervals, the filter has built in anti-aliasing.

Sampling IF filters can be designed for high RF image rejection without additional digital-correction techniques. In multimode radio applications, the sampling IF filter can be programmable, to eliminate several off-chip filters.

The sampling IF filter presented here represents a valuable breakthrough because superior in performance of both SC and gm-C filters. The sampling IF filter presented above consumes less power than an equivalent gm-C filter and is more stable than an equivalent SC filter.

Although the sampling IF filter approach can be applied to a variety of different systems, this presentation deals specifically with a sampling IF filter for an integrated Bluetooth Rx with a 13-MHz reference. The filter provides a 3-dB bandwidth of 480 kHz and out-of-band rejection of 50 dB for all undesired channels except the image frequency at −1 MHz (from the passband center frequency). For channels that are 3 MHz or more away from the desired channel, the filter provides at least 55-dB attenuation.

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As an example, a filter was chosen with a 1-MHz sampling frequency with a 13-MHz option and a 2-MHz IF. The 13-MHz option allows initial 13-MHz sampling until the phase of the data clock is found and then switching to 1-MHz sampling to conserve power. Since the preamble of a Bluetooth packet is short compared to the length of a packet, the power savings for the filter and the downstream digital signal processor (DSP) can be substantial.

When designing a Bluetooth filter there is a trade-off between adjacent-channel interference (ACI) and ISI (see table). Generally, as the filter bandwidth narrows, the ISI increases; as the filter bandwidth increases, so does the ACI. ISI is also dependent upon the group delay of the filter. Because a sampling IF filter is a finite-impulse-response (FIR) filter, the group delay is a constant value. Therefore, it is possible to design a narrowband filter while maintaining low ISI. Referring again to Fig. 1, it is possible to design an ideal Bluetooth FIR filter with analog tap coefficients and then quantize these analog values to discrete digital values. These quantized digital values will then be applied to the P+, P-, or P0 inputs of the circuit.

The channel-selection filter has a sufficiently narrow bandwidth to serve as an anti-aliasing filter as well. Obtaining this level of stop-band rejection close to the passband would typically require a seventh-order or higher filter.

There are two distinct disadvantages in using high-order multipole filters. They are very sensitive to process and temperature variations, so that chip yields will be low and iterations may be necessary to center the design. The other disadvantage is that each stage must be very linear to prevent intermodulation distortion (IMD). Conventional approaches to achieve this linearity typically require high power consumption.

In Fig. 2, the red line represents the response of the filter with no process or temperature variations included. The blue lines represent the effects of component mismatch and all other circuit and temperature variations. The filter exhibits almost 2 MHz of bandwidth.

A sampling IF filter also has the benefit of 48 dB of AGC. The filter's gain is adjustable in 30-dB steps by means of a 4-b control word.


  1. Mayank Garg and Sushant Suryagandh, "A switched capacitor bandpass filter for a Bluetooth wireless receiver," University of Southern California at Los Angeles website,
  2. Pietro Andreani and Sven Mattisson, "A CMOS gm-C polyphase filter with high image-band rejection,"
  3. Pietro Andreani and Sven Mattisson, "A CMOS gm-C IF filter for Bluetooth,"
  4. Sami Karvonen, Thomas Riley, and Juha Kostamovaara, "Charge sampling mixer with delta-sigma quantized impulse response," ISCAS 2002 IEEE International Symposium on Circuits and Systems, May 26-29, 2002, Session 1299.
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