Quadrature phase network

Abstract

A phase shifter comprises a differential quadrature all-pass filter (QAF) including a balanced input port and two balanced output ports. A quadrature phase shift is manifested between the balanced output ports. The phase shifter also comprises a resistance-capacitance polyphase filter (PPF) section defining two balanced input ports and two balanced output ports. The balanced input ports of the PPF are coupled to the balanced output ports of the QAF. The combination exhibits broad bandwidth and relatively low ohmic loss.

Description

BACKGROUND OF THE INVENTION

Quadrature phase-shifting networks are widely used in electronic systems. Very often, the overall bandwidth of the electronic system will depend upon the bandwidth of the quadrature phase-shifting network.

One well-known type of quadrature phase-shifting network is the coupled transmission line, which includes two quarter-wavelength unbalanced transmission lines, the “center” conductors of which are placed in physical proximity so as to provide coupling. Such coupled transmission-line phase shifters have a bandwidth in the range of ten percent.

Many modern electronic systems are desirably implemented in the form of monolithic integrated circuits. As such, the phase shifters must provide the desired phase shift while defined on, or as part of, a monolithic integrated circuit. Such integrated circuits may have substrates made from semiconductor material, such as silicon. Semiconductor, when used as a substrate for passive electronic components, such as capacitors or inductors, tends to introduce attenuation or ohmic losses, which undesirably affect the operation.

There are two other well-known types of quadrature phase shifter in addition to the coupled-transmission-line quadrature phase shifters. These include the all-pass filter and the polyphase network. FIG. 1 illustrates a prototype or single stage of the all-pass phase-shifting network 10. In FIG. 1, an all-pass phase shifting network 10 includes a balanced two-conductor “input” port 12 with two nodes or terminals 12₁ and 12₂. A pair 16 of non-coupled inductors includes inductor elements 16₁ and 16₂. Inductor element 16₁ defines first and second terminals 16₁₁ and 16₁₂. Inductor element 16₂ defines first and second terminals 16₂₁ and 16₂₂. Terminal 16₁₁ of inductor element 16₁ is connected to terminal 12₁, and terminal 16₂₂ of inductor element 16₂ is connected to terminal 12₂. All-pass phase shifting network 10 of FIG. 1 also includes a further pair of balanced “output” ports 14₁ and 14₂ of a set 14 of output ports. Output port 14₁ defines I+ and I− terminals 14₁₁ and 14₁₂, respectively, and output port 14₂ defines Q− and Q+ terminals 14₂₁ and 14₂₂, respectively. Terminal 16₁₂ of inductor element 16₁ is connected by way of a conductive path 20₂ to terminal 14₂₂, and terminal 16₂₁ of inductor element 16₂ is connected by way of a conductive path 20₁ to terminal 14₂₁. A capacitor 18₁ is connected “between” terminals 12₁ and 14₁₁, and a capacitor 18₂ is connected between terminals 12₂ and 14₁₂. A resistor 22₁ is connected “between” terminals 14₁₁ and 14₂₁, and a resistor 22₂ is connected between terminals 14₁₂ and 14₂₂.

The mutually 90° phase shifted signals appear at output ports 14₁ and 14₂. More particularly, with respect to FIG. 1, the output I+ at terminal 14₁₁ represents zero (0) degree phase shift. The output I− at terminal 14₁₂ represents −180 degree phase shift. The output Q+ at terminal 14₂₂ represents −90 degree phase shift. And the output Q− at terminal 14₂₂ represents −270 degree phase shift. Such a single stage of differential quadrature all-pass filter exhibits a bandwidth of about 2:1, and a through loss or attenuation of about five (5) dB. It should be noted that the loss of 5 dB is attributable to both ohmic or heat losses and to power division. That is, the applied power is divided among two output ports, so the power available at any given output port will in theory be only one-half of the applied power. This corresponds to a theoretical loss of 3 dB regardless of the efficiency of the circuit.

It should be noted that the terms “between,” “across,” and other terms such as “parallel” have meanings in an electrical context which differ from their meanings in the field of mechanics or in ordinary parlance. More particularly, the term “between” in the context of signal or electrical flow relating to two separate devices, apparatuses or entities does not relate to physical location, but instead refers to the identities of the source and destination of the flow. Thus, flow of signal “between” A and B refers to source and destination locations, and the flow itself may be by way of a path which is nowhere physically located between the locations of A and B. The term “between” can also define the end points of the electrical field extending “across” or to points of differing voltage or potential, and the electrical conductors making the connection need not necessarily lie physically between the terminals of the source. Similarly, the term “parallel” in an electrical context can mean, for digital signals, the simultaneous generation on separate signal or conductive paths of plural individual signals, which taken together constitute the entire signal. For the case of current, the term “parallel” means that the flow of a current is divided to flow in a plurality of separated conductors, all of which are physically connected together at disparate, spatially separated locations, so that the current travels from one such location to the other by plural paths, which need not be physically parallel.

In addition, discussions of circuits necessarily describe one element at a time, as language is understood in serial time. Consequently, a description of two interconnected elements may describe them as being in “series” or in “parallel,” which may be true for the two elements described. However, further description of the circuit may implicate other interconnected devices, which when connected to the first two devices may result in current flows which contradict the “series” or “parallel” description of the original two devices. This is an unfortunate result of the limitations of language, and all descriptions herein should be understood in that context.

Also, the term “coupled” as used herein includes electrical activity extending from one element to another element either by way of an intermediary element or in the absence of any intermediary element.

The terms “input” and “output” in the case of passive networks such as those of FIG. 1 are for ease of identification and are not necessarily descriptive of the use, as such networks are “reciprocal,” in that their actions are independent of the direction of energy flow therethrough.

FIG. 2A illustrates a prototype of a single-pole polyphase filter 210, and FIG. 2B illustrates a prototype of a double-pole polyphase filter 250. In FIG. 2A, single-pole polyphase filter 210 includes a balanced input port 212 including input + terminal 212₁ and − terminal 212₂, and output ports 214₁ and 214₂. Output port 214₁ defines I+ terminal 214₁₁ and I− terminal 214₁₂, and output port 214₂ defines Q+ terminal 214₂₁ and Q− terminal 214₂₂. A resistor 222₁ is connected between terminals 212₁ and 214₁₁. A resistor 222₂ is connected between terminals 212₁ and 214₂₁, a resistor 222₃ is connected between terminals 212₂ and 214₁₂, and a resistor 222₄ is connected between terminals 212₂ and 214₂₂. Also, a capacitor 218₁ is connected between terminals 212₁ and 214₂₁, a capacitor 218₂ is connected between terminals 212₁ and 214₁₂, a capacitor 218₃ is connected between terminals 212₂ and 214₂₂, and a capacitor 218₄ is connected between terminals 212₂ and 214₁₁.

The single-pole arrangement of FIG. 2A provides quadrature phase shift between ports 214₁ and 214₂, but with relatively limited bandwidth because of its single-stage nature. More particularly, with respect to FIG. 2A, the output I+ at terminal 214₁₁ represents zero (0) degree phase shift. The output I− at terminal 214₁₂ represents +180 degree phase shift. The output Q+ at terminal 214₂₁ represents +90 degree phase shift. And the output Q− at terminal 214₂₂ represents +270 degree phase shift.

The multistage filter 250 of FIG. 2B provides greater bandwidth than the single-stage filter 210 of FIG. 2A. Filter 250 of FIG. 2B includes a balanced input port 252 with + terminal 252₁ and − terminal 252₂, and balanced output ports 254₁ and 254₂. Output port 254₁ includes I+ terminal 254₁₁ and I− terminal 254₁₂, and output port 254₂ includes Q+ terminal 254₂₁ and Q− terminal, 254₂₂. A resistor 272₁ of a set 272 of resistors extends, or is coupled, from terminal 252₁ to a node 280₁, a resistor 272₂ extends from terminal 252₁ to a node 280₂, a resistor 272₃ extends from terminal 252₂ to a node 280₃, and a resistor 272₄ extends from terminal 252₂ to a node 280₄. A capacitor 268₁ of a set 268 of capacitors is coupled between terminal 252₁ and node 280₂, a capacitor 268₂ is coupled between terminal 252₁ and node 280₃, a capacitor 268₃ is coupled between terminal 252₂ and node 280₄, and a capacitor 268₄ is coupled between terminal 252₂ and node 280₁. Also in FIG. 2B, a resistor 272₅ of set 272 of resistors is coupled from node 280₁ to terminal 254₁₁, a resistor 272₆ is coupled from node 280₂ to terminal 254₂₁, a resistor 272₇ is coupled from node 280₃ to terminal 254₁₂, and a resistor 272₈ is coupled from node 280₄ to terminal 254₂₂. A capacitor 268₅ of set 268 of capacitors is coupled between node 280₁ and terminal 254₂₁, a capacitor 268₆ is coupled between node 280₂ and terminal 254₁₂, a capacitor 268₇ is coupled between node 280₃ and terminal 254₂₂, and a capacitor 268₈ is coupled between node 280₄ and terminal 254₁₁.

The bandwidth of filter 250 of FIG. 2B is about 3:1. However, the attenuation or through loss is about 12 to 15 decibels (dB). Quadrature filters are desired which provide relatively low through loss or attenuation and broad bandwidth.

SUMMARY OF THE INVENTION

A quadrature filter network includes a differential quadrature all-pass filter defining an input port and a pair of output ports at which nominally mutually quadrature signals are generated. The mutually quadrature signals serve as inputs to a resistance/reactance filter defining a pair of input ports and at least one output port, wherein the pair of input ports of the resistance/reactance filter are coupled to the pair of output ports of the quadrature all-pass filter.

The output ports of the quadrature all-pass filter further define a first output port having an I− terminal and an I+ terminal, and a second output port having a Q− terminal and a Q+ terminal. The input ports of the resistance/reactance filter define a first input port having an I− terminal and an I+ terminal, and a second input port having a Q− terminal and a Q+ terminal.

The I− output terminal of the quadrature all-pass filter is connected to the I− input terminal of the resistance/reactance filter. The I+ output terminal of the quadrature all-pass filter is connected to the I+ input terminal of the resistance/reactance filter. The Q− output terminal of the quadrature all-pass filter is connected to the Q+ input terminal of the resistance/reactance filter. The Q+ output terminal of the quadrature all-pass filter is connected to the Q− input terminal of the resistance/reactance filter.

In one embodiment, a phase-shifter includes a quadrature all-pass filter and a poly-phase filter. The quadrature all-pass filter is configured to receive a radio frequency signal and output I and Q outputs. The I output further defines an I− output terminal and an I+ output terminal, while the Q output further defines a Q− output terminal and a Q+ output terminal.

The poly-phase filter circuit is coupled to the quadrature all-pass filter circuit. The poly-phase filter circuit includes an I− input terminal, an I+ input terminal, a Q− input terminal and a Q+ input terminal. The poly-phase filter circuit is configured to receive the output of the quadrature all-pass filter circuit as inputs. The I− output terminal of the quadrature all-pass filter circuit is coupled to the I− input terminal of the poly-phase filter circuit. The I+ output terminal of the quadrature all-pass filter circuit is coupled to the I+ input terminal of the poly-phase filter circuit. The Q− output terminal of the quadrature all-pass filter circuit is coupled to the Q+ input terminal of the poly-phase filter circuit. The Q+ output terminal of the quadrature all-pass filter circuit is coupled to the Q− input terminal of the poly-phase filter circuit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified schematic diagram of a prior-art differential quadrature all-pass filter or phase shifter;

FIG. 2A is a simplified schematic diagram of a prior-art single-pole polyphase filter, and FIG. 2B is a simplified schematic diagram of a prior-art two-pole polyphase filter;

FIG. 3A is a simplified conceptual block diagram of a filter according to an aspect of the disclosure, and FIG. 3B is a corresponding schematic diagram.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 3A is a simplified block diagram illustrating a network or filter 308 according to an aspect of the disclosure. In FIG. 3A, a block 359 represents a differential quadrature all-pass filter (QAF) or network. Block or network 359 includes a balanced input port 312 with + and − terminals, ports, electrodes or conductors 312₁ and 312₂, respectively. QAF block 359 also comprises first and second balanced output ports 350₁ and 350₂, where balanced output port 350₁ is the I port and balanced output port 350₂ is the Q port. Output port 350₁ has I+ or first terminal 350₁₁ and I− or second terminal 350₁₂, respectively. Output port 350₂ has Q+ or first terminal 350₂₁ and Q− or second terminal 350₂₂.

Network 308 of FIG. 3A also includes a modified polyphase filter section (PPF) 370. PPF 370 includes first and second balanced input ports 360₁ and 360₂, respectively. Input port 360₁ comprises I+ or first terminal 360₁₁ and I− or second terminal 360₁₂. Input port 360₂ defines Q+ terminal 360₂₁ and Q− terminal 360₂₂. PPF 370 also has an I output port 314₁ and a Q output port 314₂. I output port 314₁ comprises I+ terminal 314₁₁ and I− terminal 314₁₂, and Q output port 314₂ comprises Q+ terminal 314₂₁ and Q− terminal 314₂₂. As illustrated in FIG. 3A, I+ output terminal 350₁₁ of QAF 359 is connected to I+ input terminal 360₁₁ of PPF 370. I− output terminal 350₁₂ of QAF 359 is connected to I− input terminal 360₁₂ of PPF filter 370. Q+ output terminal 350₂₁ of QAF filter 359 is connected to Q− terminal 360₂₂ of PPF filter 370, and Q− output terminal 350₂₂ is connected to Q+ input terminal 360₂₁ of PPF filter 370.

FIG. 3B illustrates some details of a phase shifter according to an aspect of the disclosure. Elements of FIG. 3B corresponding to those of FIG. 3A are designated by like reference alphanumerics. In filter portion 359 of FIG. 3B, an inductor 316₁ is coupled between terminal or node 312₁ and terminal or node 350₂₁, and an inductor 316₂ is coupled between terminal or node 312₂ and terminal or node 350₂₂. A capacitor 318₁ is coupled between terminal 312₁ and node 350₁₁, and a capacitor 318₂ is coupled between terminal 312₂ and node 350₁₂. A resistor 322₁ is connected between nodes 350₁₁ and 350₂₂, and a resistor 322₂ is connected between nodes 350₂₁ and 350₁₂. The outputs at nodes 350₁₁, 350₁₂, 350₂₁, and 350₂₂ represent the I+, I−, Q+, and Q− signals, respectively, from filter portion 359.

Also in FIG. 3B, filter portion 370 includes a resistor 372₁ connected between terminal or node 360₁₁ and terminal 314₁₁, a resistor 372₂ connected between terminal or node 360₂₁ and terminal 314₂₁, a resistor 372₃ connected between terminal or node 360₁₂ and terminal 314₁₂, and a resistor 372₄ connected between terminal or node 360₂₂ and terminal 314₂₂. Also, a capacitor 368₁ is connected between terminal or node 360₁₁ and terminal 314₂₁, a capacitor 368₂ is connected between terminal or node 360₂₁ and terminal 314₁₂, a capacitor 368₃ is connected between terminal or node 360₁₂ and terminal 314₂₂, and a capacitor 368₄ is connected between terminal or node 360₂₂ and terminal 314₁₁. The output I+ at terminal 314₁₁ represents zero (0) degree phase shift. The output I− at terminal 314₁₂ represents +180 degree phase shift. The output Q+ at terminal 314₂₁ represents +90 degree phase shift. And the output Q− at terminal 314₂₂ represents +270 degree phase shift.

In the arrangement of FIG. 3B, the element values are as follows. The values of inductors 316₁ and 316₂ are the same, namely 621 picohenries (pH). The capacitors 318₁ and 318₂ are of the same value, namely 612 femtofarads (fF). Resistors 322₁ and 322₂ both have a value of 63 ohms. Resistors 372₁, 372₂, 372₃, and 372₄ are each 84 ohms. Capacitors 368₁, 368₂, 368₃, and 368₄ are each 71.8 fF. With these values, the bandwidth is 7 to 22 gigahertz (GHz) without optimization, and optimized embodiments have achieved a bandwidth extending from about 5 to 25 GHz. The through loss is about 7 dB. Thus, the disclosed arrangement provides bandwidth equal to or better than the two-pole polyphase filter of the prior art, with losses which are improved (reduced) by about 5 to 8 dB. By comparison with the 2:1 bandwidth of the differential quadrature all-pass filter, the bandwidth of the disclosed arrangement is, or at least can be, more than 3:1 and as much as 5:1. The through loss of 7 dB is only about two dB worse than the QAF.

Thus, a quadrature filter network (308) according to an aspect of the disclosure comprises a differential quadrature all-pass filter (359) defining an input port (312) and a pair of output ports (350₁, 350₂) at which nominally mutually quadrature signals are generated. The quadrature filter also comprises a resistance-reactance filter (370). The resistance-reactance filter (370) defines a pair of input ports (360₁, 360₂), and also defines at least an output port. The pair of input ports (360₁, 360₂) of the resistance-reactance filter (370) is coupled to the pair of output ports (350₁, 350₂) of the differential quadrature all-pass filter (359). In one embodiment, the output ports of the differential quadrature all-pass filter and the input ports of the resistance-reactance filter are balanced.

A phase shifter (308) according to another aspect of the disclosure comprises a differential filter (359) coupled to a polyphase filter (370). The differential filter (359) defines a balanced input port (312) and first (350₁) and second (350₂) balanced intermediate or output ports. The balanced input port (312) defines first (312₁) and second (312₂) terminals. The first (350₁) balanced intermediate port defines first (350₁₁) and second (350₁₂) intermediate nodes, and the second (350₂) balanced intermediate port defines first (350₂₁) and second (350₂₂) intermediate nodes. The differential filter (359) further comprises a first capacitor (318₁) coupled from the first terminal (312₁) of the balanced input port (312) to the first node (350₁₁) of the first intermediate port (350₁), an inductor (316₁) coupled from the first terminal (312₁) of the balanced input port (312) to the first node (350₂₁) of the second intermediate port (350₂), and a resistor (322₁) coupled from the first intermediate node (350₁₁) of the first intermediate port (350₁) to the second intermediate node (350₂₂) of the second intermediate port (350₂). The differential filter (359) further comprises a second capacitor (318₂) coupled from the second terminal (312₂) of the balanced input port (312) to the second intermediate node (350₁₂) of the first intermediate port (350₁), an inductor (316₂) coupled from the second terminal (312₂) of the balanced input port (312) to the second node (350₂₂) of the second intermediate port (350₂), and a resistor (322₂) coupled from the first intermediate node (350₂₁) of the second intermediate port (350₂) to the second node (350₁₂) of the first intermediate port (350₂). The polyphase filter (370) comprises first (360₁) and second (360₂) balanced input ports and first (314₁) and second (314₂) balanced output ports. The first balanced input port (360₁) of the polyphase filter (370) defines first (360₁₁) and second (360₁₂) nodes, and the second balanced input port (360₂) of the polyphase filter (370) defines first (360₂₁) and second (360₂₂) nodes. The first node (360₁₁) of the first balanced input port (360₁) of the polyphase filter (370) is coupled to the first intermediate node (350₁₁) of the first intermediate port (350₁) of the differential filter (359). The second intermediate node (360₁₂) of the first balanced input port (360₁) of the polyphase filter (370) is coupled to the second intermediate node (350₁₂) of the first intermediate or output port (350₁) of the differential filter (359). The first node (360₂₁) of the second balanced input port (360₂) of the polyphase filter (370) is coupled to the second intermediate node (350₂₂) of the second intermediate port (350₂) of the differential filter (359), and the second intermediate node (360₂₂) of the second balanced input port (360₂) of the polyphase filter (370) is coupled to the first intermediate node (350₂₁) of the second intermediate or output port (350₂) of the differential filter (359). The second node (360₁₂) of the first input port (360₁) of the polyphase filter (370) is coupled by a resistor (372₃) to the second terminal (314₁₂) of the first output port (314₁) of the polyphase filter (370). The first node (360₁₁) of the first input port (360₁) of the polyphase filter (370) is coupled by a resistor (372₁) to the first terminal (314₁₁) of the first output port (314₁) of the polyphase filter (370). The second node (360₂₂) of the second input port (360₂) of the polyphase filter (370) is coupled by a resistor (372₄) to the second terminal (314₂₂) of the second output port (314₂) of the polyphase filter (370). The first node (360₂₁) of the second input port (360₂) of the polyphase filter (370) is coupled by a resistor (372₂) to the first terminal (314₂₁) of the second output port (314₂), of the polyphase filter (370). The second node (360₁₂) of the first input port (360₁) of the polyphase filter (370) is coupled by a capacitor (368₃) to the second terminal (314₂₂) of the second output port (314₂) of the polyphase filter (370). The first node (360₁₁) of the first input port (360₁) of the polyphase filter (370) is coupled by a capacitor (368₁) to the first terminal (314₂₁) of the second output port (314₂) of the polyphase filter (370). The second node (360₂₂) of the second input port (360₂) of the polyphase filter (370) is coupled by a capacitor (368₄) to the first terminal (314₁₁) of the first output port (314₁) of the polyphase filter (370), and the first node (360₂₁) of the second input port (360₂) of the polyphase filter (370) is coupled by a capacitor (368₂) to the second terminal (314₁₂) of the first output port (314₁) of the polyphase filter (370). In a particular embodiment of the phase shifting network (308), each of the capacitors of the differential filter (359) has a value near 612 femtofarads (fF), or each of the inductors of the differential filter (359) has a value near 621 picohenries (pH), or each of the resistors of the differential filter (359) has a value near 63 ohms. In a particular embodiment, each of the capacitors of the polyphase filter (370) has a value near 72 fF, or each of the resistors of the polyphase filter (370) has a value near 84 ohms.

Claims

1. A quadrature filter network comprising: a differential quadrature all-pass filter defining an input port and a pair of output ports comprising a first output port having an output I+ terminal, and an output I− terminal and a second output port having an output Q+ terminal, and an output Q− terminal, at which nominally mutually quadrature signals are generated;a resistance-reactance filter defining a pair of input ports, comprising a first input port having an input I+ terminal, and an input I− terminal; and a second input port having an input Q+ terminal, and an input Q− terminal and also defining at least an output port, said pair of input ports of said resistance-reactance filter being coupled to said pair of output ports of said differential quadrature all-pass filter, andwherein the input I+ terminal of the resistance reactance filter is connected to the output I+ terminal of the quadrature all-pass filter;the input I− terminal of the resistance reactance filter is connected to the output I− terminal of the quadrature all-pass filter;the input Q+ terminal of the resistance reactance filter is connected to the output Q− terminal of the quadrature all-pass filter; andthe input Q− terminal of the resistance reactance filter is connected to the output Q+ terminal of the quadrature all-pass filter.

2. The quadrature filter network of claim 1, wherein said output ports of said differential quadrature all-pass filter and said input ports of said resistance-reactance filter are balanced.

3. A phase-shifter comprising: a quadrature all-pass (QAP) filter circuit configured to receive a radio frequency input signal at an In+ terminal and at an In− terminal and configured to output I and Q outputs, wherein the I output is output at an I+ output terminal and at an I− output terminal, and the Q output is output at a Q+ output terminal and a Q− output terminal;a poly-phase filter (PPF) circuit coupled to said QAP filter circuit, the PPF circuit having:I and Q input ports, the I input port having an I+ input terminal and an I− input terminal; and the Q input port having a Q+ input terminal and a Q− input terminal; andI and Q output ports, the I output port having an I+ output terminal and an I− output terminal; and the Q output port having a Q+ output terminal and a Q− output terminal;wherein the PPF circuit is configured to receive the I and Q outputs of the QAP filter circuit at the I and Q input ports of the PPF circuit,wherein the I+ output terminal of the QAP filter circuit is coupled to the I+ input terminal of the PPF circuit, the I− output terminal of the QAP filter circuit is coupled to the I− input terminal of the PPF, the Q+ output terminal of the QAP filter is coupled to the Q− input terminal of the PPF circuit, and the Q− output terminal of the QAP filter circuit is coupled to the Q+ input terminal of the PPF circuit.

4. The phase-shifter of claim 3, wherein the QAP filter circuit comprises an inductive/capacitive filter.

5. The phase-shifter of claim 3, wherein the PPF filter circuit comprises a resistance-reactance circuit.

6. The phase-shifter of claim 3, wherein the input terminals of the QAP filter circuit are balanced.

7. A method of producing a quadrature phase shifted radio frequency signal comprising: receiving a radio frequency input signal at a differential quadrature all-pass (QAP) filter circuit;outputting from the QAP circuit, mutually quadrature signals at an I output at an I+ terminal and an I− terminal, and a Q output at a Q+ terminal and a Q− terminal;coupling the I+ terminal to an I+ input terminal of a poly-phase filter (PPF) circuit; and coupling the I− terminal to an I− input terminal of the PPF circuit;coupling the Q+ terminal to a Q− input terminal of the PPF circuit; and coupling the Q− terminal to a Q+ input terminal of the PPF circuit;outputting from the PPF circuit, mutually quadrature signals at an I output from an I+ output terminal and an I− output terminal, and a Q output from a Q+ output terminal and a Q− output terminal.

8. The method of claim 7, wherein said output ports of said differential quadrature all-pass filter and said input ports of said PPF circuit are balanced.