An apparatus (100; 200; 300; 400), comprising: a first mixer (110; 210; 320; 420) configured and arranged to down-convert a radio frequency (RF) signal to produce a first intermediate frequency (IF) signal having exactly a first number, M, of equally spaced phase components; a second mixer (120; 220; 330; 430) configured and arranged to down-convert the first IF signal to produce a second IF signal having exactly a second number, N, of equally spaced phase components, wherein N > M; and a plurality, O, of summing circuits (130; 230; 350; 470), each configured and arranged to combine various ones of phase components of the second IF signal to produce a respective phase component of a third IF signal, the third IF signal being a balanced quadrature phase IF signal; wherein each summing circuit comprises a trans-impedance amplifier including a set of resistors arranged to adjust weights of said various ones of phase components prior to summing; wherein N=3 or 6 and each of the plurality of summing circuits (130; 230; 350; 470) is arranged to add two of the phase components produced by the second mixer to produce a phase component of the third IF signal, wherein the first mixer (110; 210; 320; 420) is configured and arranged to subtract a first local oscillator (LO) signal from the RF signal to produce the first IF signal; and the second mixer (120; 220; 330; 430) is configured and arranged to subtract a second LO signal from the first IF signal to produce the second IF signal, the second LO signal has a frequency that is less than a frequency of the first LO signal, and wherein the frequency of the first LO signal is 3/2 the frequency of the second LO signal such that N = 3 ∗ M. a first mixer (110; 210; 320; 420) configured and arranged to down-convert a radio frequency (RF) signal to produce a first intermediate frequency (IF) signal having exactly a first number, M, of equally spaced phase components; a second mixer (120; 220; 330; 430) configured and arranged to down-convert the first IF signal to produce a second IF signal having exactly a second number, N, of equally spaced phase components, wherein N > M; and a plurality, O, of summing circuits (130; 230; 350; 470), each configured and arranged to combine various ones of phase components of the second IF signal to produce a respective phase component of a third IF signal, the third IF signal being a balanced quadrature phase IF signal; wherein each summing circuit comprises a trans-impedance amplifier including a set of resistors arranged to adjust weights of said various ones of phase components prior to summing; wherein N=3 or 6 and each of the plurality of summing circuits (130; 230; 350; 470) is arranged to add two of the phase components produced by the second mixer to produce a phase component of the third IF signal, wherein the first mixer (110; 210; 320; 420) is configured and arranged to subtract a first local oscillator (LO) signal from the RF signal to produce the first IF signal; and the second mixer (120; 220; 330; 430) is configured and arranged to subtract a second LO signal from the first IF signal to produce the second IF signal, the second LO signal has a frequency that is less than a frequency of the first LO signal, and wherein the frequency of the first LO signal is 3/2 the frequency of the second LO signal such that N = 3 ∗ M. <EOS>