Complex filter with higher order pole

Pairs of second-order filters with feedback and cross coupling may be used to implement pairs of complex poles. The cross coupling may be frequency-dependent cross coupling or frequency-independent cross coupling. Frequency independent cross coupling may include coupling an internal node of a biquad filter. The pairs of second-order filters can be used together to form a complex filter. The complex filter can be used to readily provide higher order poles. The resulting complex filter can achieve higher order poles while offering reduced circuit complexity.

TECHNICAL FIELD

The invention relates to complex filters, and more particularly, to complex filters with higher order poles.

BACKGROUND

Complex filters may be useful in a number of applications, such as RF devices. For example, a receiver may use one or more complex filters to reduce noise or filter out adjacent channels. In addition, complex filters may be used to accept a complex signal and separate the real part of the signal from the imaginary part of the signal.

Circuits that act as complex filters may generate complex poles. A complex pole may be useful in circuits that filter quadrature signals, for example, to provide an asymmetric response about DC. Circuits with complex poles may generate quadrature signals from a single signal and perform amplitude/phase filtering of the quadrature signals. The quadrature signals may be generated by quadrature downconversion or in preparation for quadrature upconversion.

Several techniques exist for generating a single complex pole. For example, cross coupling may be used between pairs of real poles. Another technique involves converting a pair of ladder-derived real filters into a frequency-shifted complex filter by using cross coupling between the real filters. In both techniques described, frequency-independent cross coupling and single real poles are used.

SUMMARY

In general, the invention is directed to a technique for creating a complex electrical filter, which has an asymmetric response about DC. The complex filter may be especially useful in a wireless communication system. The technique involves the use of pairs of second-order filters, such as biquadratic (biquad) filters, with feedback and cross coupling. The cross coupling may be frequency-dependent cross coupling or frequency-independent cross coupling. Frequency-independent cross coupling may involve coupling to an internal node of the biquad filter. The complex filter can be used to readily provide higher order poles.

A complex filter in accordance with the invention may provide one or more advantages. For example, the invention allows biquad-derived real filters to be made into complex filters in a straightforward manner. The resulting complex filter can achieve higher order poles while offering reduced circuit complexity. In addition, the shape of a filtered signal can be maintained over a range of operating conditions because pairs of poles in the complex filter move together with changes in operating conditions. Accordingly, the filter may offer reduced sensitivity. In some embodiments, a second-order complex filter may be realized without a differentiator, providing reductions in the chip area consumed by the filter. Additionally, elimination of the differentiator may result in reduced noise.

In one embodiment, the invention provides a complex filter comprising an input port to receive a complex input signal, a first output port that produces a real output component, a second output port that produces an imaginary output component, a pair of second order filters, wherein each of the second order filters receives a sum of at least a portion of the input signal, and an amplified portion of one of the first and second output components.

In another embodiment, the invention provides a method comprising receiving a complex input signal, generating a real output component of the complex input signal, generating an imaginary output component of the complex input signal, passing a sum of at least a portion of the complex input signal and an amplified portion of one of the first and second output components through each of a pair of second order filters to produce the complex input signal and the complex output signal.

In a further embodiment, the invention provides a wireless receiver comprising an antenna to receive a wireless input signal, an amplifier to amplify the wireless input signal, and a complex filter having an input port to receive the wireless input signal, a first output port that produces a real output component of the wireless signal, a second output port that produces an imaginary output component of the wireless signal, and a pair of second order filters, wherein each of the second order filters receives a sum of at least a portion of the input signal, and an amplified portion of one of the first and second output components.

In another embodiment, the invention provides a complex filter comprising a first biquad filter, a second biquad filter, a first feedback loop between an output and input of the first biquad filter, a second feedback loop between an output and input of the second biquad filter, a cross-coupling between the first biquad filter and the second biquad filter.

DETAILED DESCRIPTION

FIG. 1is a block diagram illustrating an exemplary system10that includes a filter18for filtering complex signals. Complex filters are used in a variety of telecommunications applications, such as wireless network access points, communication chips, receivers, and transmitters. System10, which may be part of a receiver system, includes an antenna12, a low noise amplifier (LNA)14, a Radio Frequency-to-Intermediate Frequency (RF-to-IF) mixer16, a filter18, and an analog-to-digital converter19.

System10receives an RF signal via antenna12. Antenna12passes the signal to the LNA14, which amplifies the signal. Mixer16processes the amplified RF signal by down-converting the signal from a high RF frequency, such as 5.2 GHz, to an intermediate frequency, such as 10 MHz. In one embodiment, mixer16comprises a down mixer and a quadrature mixer, which are cascaded in two stages. In another embodiment, mixer16may use complex mixing to separate an imaginary image from the signal.

In one example, mixer16may be configured to process signals transmitted within a wireless network conforming to the IEEE 802.11a, 802.11b, or 802.11g standards. Mixer16generates baseband signals for in-phase and quadrature phase components of the RF signal. Mixer16passes the amplified signal to filter18, which filters out adjacent channels, alternate adjacent channels, and noise. For example, filter18may filter out negative frequencies, thereby removing negative frequency images from the signal. In one embodiment, filter18further includes a block that limits the dynamic range of system10.

Filter18may be configured to relay the filtered signal to another component, such as an analog-to-digital (A/D) converter19. A/D converter19converts the analog signal to a digital signal for additional processing, e.g., with a demodulation block. The digital signal may be further amplified and processed based on the needs of the system10.

In some applications, system10may include pairs of second-order filters with feedback and cross coupling for implementing pairs of complex poles. The cross coupling may be frequency-dependent cross coupling or frequency-independent cross coupling. The second-order filters may simultaneously perform both lowpass and highpass filtering of an input signal to selectively pass signals in particular frequency ranges.

FIG. 2is a block diagram illustrating a basic complex filter circuit20accepting a single input signal, for purposes of example. Complex filters may accept a complex input signal and separate the real part of the signal from the imaginary part of the signal. As shown inFIG. 2, complex filter22separates an input signal into an ‘I’ output component24and a ‘Q’ output component26. The ‘I’ output component24is the real component of the input signal and the ‘Q’ output component26is the imaginary component of the input signal. In one embodiment, the ‘I’ component24leads the ‘Q’ component26by approximately 90 degrees. In practice, filter circuit20may be modified in a variety of manners. For example, filter22may accept more than one input.

FIG. 3is a block diagram illustrating a basic complex filter circuit30accepting two input signals. Rather than inputting a single input signal into filter32, both ‘I’ and ‘Q’ components of an input signal are separately applied to filter32. Two or more filters22(FIG. 2) may be used together to make a higher order complex filter circuit32. For example, two complex filters may be used to make a second order complex filter, such as a biquadratic (biquad) filter. Second order filters, which include Tow-Thomas biquad filters, may be used as described below for implementing pairs of complex poles.

FIG. 4is a circuit diagram illustrating implementation of a complex filter circuit40with two second-order filters. In particular, the two second-order filters may be all-pole biquad filters. The complex filter40may include two channels, an ‘I’ channel and a ‘Q’ channel. The ‘I’ channel corresponds to a real portion of an input signal, while the ‘Q’ channel corresponds to the imaginary portion of an input signal. As shown inFIG. 4, complex filter circuit includes biquad filters42A,42B, differentiators (d/dt)46A,46B, and amplifiers Afb43A, Afb43B, Ac44A, -Ac44B, Hc45A, -Hc45B.

An all-pole biquad filter has the following transfer function:

yx=w02s2+s⁢w0Q+w02=1s2w02+sw02+1=⁢11+j⁢ww0⁢Q-w2w02
where y is the output, x is the input, wois the cut-off frequency of the biquad filter, w is the frequency, and Q is the ‘Q’ factor of the biquad filter. However, a complex all-pole biquad filter has the transfer function:

yx=11+j⁢(w-w1)w0⁢Q-(w-w1)2w02=11+j⁢ww0⁢Q-j⁢w1w0⁢Q-w2w02+2⁢w1⁢ww02-w12w02
The value wlis the frequency shift.

Feedback and cross-coupling are used in order for complex filter circuit40to produce the complex all-pole biquad filter transfer function. The gains from cross-coupling include a frequency independent term, and a term proportional to s, which is shown by (d/dt) inFIG. 4. As discussed in more detail below, the frequency dependent term may instead be implemented by using a frequency independent cross gain into an auxiliary input of a Tow-Thomas biquad.

A feedback circuit of the ‘I’ channel may include an amplifier Afb43A, which connects the output of biquad filter42A to the input of biquad filter42A. The output of Afb43A is added to the output of amplifier Ac44A and amplifier Hc45A. The sum of Afb43A, Ac44A, Hc45A and an ‘I’ component of the input signal is inputted into biquad filter42A. Maintaining consistency with the complex all-pole biquad filter transfer function, the values of amplifiers Afb, Ac, and Hc are as follows:

Afb=w12w02,
which is a frequency-independent feedback term with no j;

Ac=w1w0⁢Q,
which is a frequency-independent, feedback term from the ‘Q’ channel with no j; and

Hc=2⁢w1w02,
which is a frequency-dependent feedback term from the ‘Q’ channel with j.

The value of the output y of biquad filter42A may be expressed with respect to the input x′ of the biquad filter.

x″=y⁡(w12w02+jw1w0⁢Q-2⁢w1⁢ww02),
where x″ is the sum of Afb, Ac, and Hc.

For ease of explanation, techniques for calculating only the values of ‘I’ channel components are described. ‘Q’ channel components are calculated using similar techniques. In particular, the same principles used for the ‘I’ channel may be applied to the ‘Q’ channel, with jX as the input and jY as the output. Accordingly,FIGS. 5-7,9and10generally illustrate one-half of a complex filter for ease of illustration. The other half may be formed by another version of the illustrated filter to form the complex filter.

The complex poles of complex filter circuit40are at:

-w02⁢Q±w0⁢1-14⁢Q2*j+w1⁢j
The pair of complex poles corresponding to complex filter circuit40may move together as operating conditions change. In other words, the shape of a filtered signal may be maintained because pairs of real and imaginary poles move together, tracking one another.

FIG. 5is a diagram illustrating an exemplary second-order filter50that can be part of a complex filter. In particular, filter50may be a Tow-Thomas biquad filter, which can be used in the complex filter circuit40described above. Filter50includes inverting integrators52,54, and an inverter57. In addition, filter50includes gains51,53,55, and56, and summations58A and58B. Taken together, these components form an exemplary implementation of the unity-gain all-pole biquad transfer function. The transfer function of filter50is:

FIG. 6is a diagram illustrating an alternative second-order filter60with an auxiliary input. The filter60may be a Tow-Thomas biquad filter, which may be used in the complex filter circuit40described above. Filter60is a modified version of filter50. In particular, filter60includes an auxiliary input that is added to filter50. Filter60includes inverting integrators62,64, and an inverter67. In addition, filter60includes gains61,63,65,66, and68, and summations69A,69B, and69C. Together, these components form an exemplary implementation of the unity-gain all-pole biquad transfer function from the main input VINto the output VOUT, as well as an implementation of a differentiated version of the unity-gain all-pole biquad transfer function from the auxiliary input VAUXto the output VOUT. The transfer function of filter60from auxiliary input VAUXto output VOUTis:

VOUTVAUX=sw02s2+w0Q⁢s+w02=s⁢VOUTVIN
As seen in the transfer function of filter60, bringing a signal though the auxiliary input is equivalent to bringing s* the signal into the primary input (i.e., s multiplied by the signal into the primary input). This is equivalent to bringing the signal through a differentiator into the primary input.

FIG. 7is a schematic diagram illustrating the exemplary second-order filter70(shown conceptually as filter50inFIG. 5), which has no auxiliary input. Filter70may be a Tow-Thomas filter and fully-differential to allow inversion by cross-coupling. As shown inFIG. 7, the second-order filter70may include operational amplifiers71A,71B, resistor76, resistor77, resistor78, resistor79, resistor80, and capacitor81. More particularly, operational amplifier71A comprises input ports72A,73A, output port74A, and a capacitor75A connecting output port74A to input port72A. Likewise, operational amplifier72B comprises input ports72B,73B, output port74B, a capacitor75B connecting output port74B to input port72B, and resistor78also connecting output port74B to input port72B. Resistor77connects the output74A of operational amplifier71A to the input72B of operational amplifier71B. In addition, resistor76feeds the output74B of operational amplifier71B to the input72A of operational amplifier71A.

The ‘I’ component of the input signal passes through resistor79on the way to input72A of operational amplifier71A. Likewise, the ‘Q’ component of the output signal passes through resistor80in parallel with capacitor81on the way to input72A of operational amplifier71A. Resistor80and capacitor81may together form a differentiator. Some exemplary relationships of circuit elements in filter70are as follows:

R79=⁢1wo⁢C75⁢AR76=⁢wo(-w12+wo2)⁢C75⁢AR77=⁢-1wo⁢C75⁢BR78=⁢Qwo⁢C78⁢BR80=⁢Qw1⁢C75⁢AC81=⁢2⁢C75⁢A⁢w1w0
In the above expressions, the subscripted number refers to the reference number of the corresponding component illustrated inFIG. 7.

FIG. 8is a diagram illustrating an implementation of another complex filter circuit85. As shown inFIG. 8, complex filter circuit85includes two second-order filters. In particular, the two second-order filters may be modified Tow-Thomas biquad filters. Each biquad filter receives an auxiliary input along with a primary input. An ‘I’ channel corresponds to a real portion of an input signal, while a ‘Q’ channel corresponds to the imaginary portion of an input signal. As shown inFIG. 4, complex filter circuit includes biquad filters86A,86B, and amplifiers Afb87A, Afb87B, Ac89A, -Ac89B, Hc88A, -Hc88B.

The function of complex filter85is substantially the same as complex filter40shown inFIG. 4. However, there are some features in complex filter85that distinguish it from complex filter40. For example, complex filter85allows a simple gain to be used rather than a differentiator. In addition, the auxiliary inputs into biquad filters86A,86B cause the gain of complex filter circuit85to be frequency independent.

FIG. 9is a schematic diagram illustrating an alternative second-order filter90(shown conceptually as filter60inFIG. 6), which has an auxiliary input. Filter90may be a modified Tow-Thomas filter. As shown inFIG. 9, the second-order filter90may include operational amplifiers91A,91B, resistor96, resistor97, resistor98, resistor99, resistor100, and resistor101. More particularly, operational amplifier91A comprises input ports92A,93A, output port94A, and a capacitor95A connecting output port94A to input port92A. Likewise, operational amplifier92B comprises input ports92B,93B, output port94B, a capacitor95B connecting output port94B to input port92B, and resistor98also connecting output port94B to input port92B. Resistor97connects the output94A of operational amplifier91A the input92B of operational amplifier91B. In addition, resistor96feeds the output94B of operational amplifier91B to the input92A of operational amplifier91A.

The ‘I’ component of the input signal passes through resistor99on the way to input92A of operational amplifier91A. Likewise, the ‘Q’ component of the output signal passes through resistor100on the way to input92A of operational amplifier91A. Additionally, the auxiliary input signal passes through resistor101on the way to input92B of operational amplifier91B. Some relationships of circuit elements in complex filter90are as follows:

R99=⁢1wo⁢C95⁢AR96=⁢wo(-w12+wo2)⁢C95⁢AR97=⁢-1wo⁢C95⁢BR98=⁢Qwo⁢C95⁢BR100=⁢Qw1⁢C95⁢AR101=⁢w02⁢w1⁢C95⁢B
In the above expressions, the subscripted number refers to the reference number of the corresponding component illustrated inFIG. 9.

Filter90is very similar to filter70shown inFIG. 7. However, filter90does not use a differentiator. Instead, filter90adds an auxiliary input signal that passes through resistor101. Moreover, filter90allows a simple gain to be used in place of the differentiator. Lack of a differentiator in complex filter90may reduce the chip area required for the second-order complex filter. Additionally, there may be less noise without the differentiator.

FIG. 10is a schematic diagram illustrating an alternative second-order filter110that may be part of a complex filter. This complex filter is not specifically a Tow-Thomas filter, but rather represents a general filter. In addition, filter110accepts no auxiliary input. Second-order filter110is similar to the filter shown inFIG. 7, except that feedback resistor78has been replaced by capacitor118. Feedback resistor78connected output port74B to input port72B, whereas capacitor118connects the output114B of operational amplifier111B to input112A of operational amplifier111A. The Q factor of the filter is then set by the ratio of capacitors115B and118. In general capacitors can be made to match well, leading to a precise value for the Q factor. The value of resistor117can tune all parameters of the filter as long as all capacitors track each other. As shown inFIG. 10, the cross gains include a frequency dependent term.

As shown inFIG. 10, the second-order filter110may include operational amplifiers111A,111B, resistor116, resistor117, resistor118, resistor119, resistor120, and capacitor121. More particularly, operational amplifier111A comprises input ports112A,113A, output port114A, and a capacitor115A connecting output port114A to input port112A. Likewise, operational amplifier112B comprises input ports112B,113B, output port114B, and a capacitor115B connecting output port114B to input port112B. Resistor117connects the output114A of operational amplifier111A the input112B of operational amplifier111B. In addition, resistor116and capacitor118feed the output114B of operational amplifier111B to the input112A of operational amplifier111A.

The ‘I’ component of the input signal passes through resistor119on the way to input112A of operational amplifier111A. Likewise, the ‘Q’ component of the output signal passes through resistor120in parallel with capacitor121on the way to input112A of operational amplifier111A. Resistor120and capacitor121may together form a differentiator. Some relationships of circuit elements in complex filter110are as follows:

R119=⁢1wo⁢C115⁢AR116=⁢w0(-w12+wo2)⁢C115⁢AR117=⁢-1wo⁢C115⁢BR120=⁢Qw1⁢C115⁢AC121=⁢2⁢C115⁢A⁢w1w0C118=⁢C115⁢AQ
In the above expressions, the subscripted number refers to the reference number of the corresponding component illustrated inFIG. 10.

FIG. 11is a graph illustrating a frequency response130of an exemplary second-order complex filter. The second-order complex filter may behave as a bandpass filter. In particular, the filter may filter out any unwanted frequencies. In one example, the filter allows only signals within a band of real frequencies to pass. The frequency response130shows a band of frequencies that are allowed to pass through a complex filter. As shown, the magnitude131of the frequency response130is greatest between frequency132and frequency133. In one embodiment, the maximum magnitude131of the frequency response may be approximately zero decibels. Depending on the characteristic of the bandpass filter, a number of frequency ranges may pass through the filter. For example, frequency132may be approximately zero MHz, and frequency133may be approximately 20 MHz.

The frequency response130of the second-order complex filter may be substantially the same regardless of how the filter is implemented. For example, a Tow-Thomas implementation using a differentiator, a Tow-Thomas implementation using the auxiliary input, a high-Q biquad using a differentiator, a high-Q biquad using an auxiliary input, a different type of biquad using a differentiator, or a different type of biquad whose first stage is an integrator, all give the same frequency response. By design, any of the filters described above may conform to the principles of a bandpass filter.