Thank you, Ray.
I'm familiar with the concepts of HP (and LP) filters.
As I said ... I couldn't see the relevance of your introducing a coupling cap into a discussion about RIAA network phase changes. But now I (sorta) can. 🙂
The entire circuit IS the RIAA network.
Sometimes the HP filters in the phono circuit are tuned to form a steep subsonic HP filter.
Sometimes the HP filters in the phono circuit are tuned to form a steep subsonic HP filter.
Nope, that adds even more phase deviation, per your question.
The entire phono circuit is the RIAA response, not just the few RC components in the RIAA calculation.
The entire phono circuit is the RIAA response, not just the few RC components in the RIAA calculation.
Ray, I'm aware of the maths that say a capacitor delivers a 90 deg phase shift ... but I've just done some measurements which suggests a coupling cap doesn't add any phase change to the output! So I am confused! 🙁 Perhaps you can 'unconfuse' me?
By way of background ... I build a head amp (ie. a gain stage which allows a LOMC to be used with an MM phono stage). It's a friend's design - not mine - but, following a medical episode about 10 years ago, he no longer wishes to spend his time constructing stuff; rather, he likes to spend his time on the computer, designing new amps. So I took over the construction (and supply) of this head amp.
Anyway, the head amp consists of a single gain stage (jfet, with CCS on top). Hence ... it inverts phase 180 deg - see here:
The small 1kHz wave is the input - about 30mV; the large sine wave is the output - about 400mV.
As you can see ... the output signal is 180 deg out of phase with the input signal.
The below picture, however, is:
* the same output as in the previous pic (taken from the head amp's output RCA sockets) at the top
* with the bottom sine wave being the signal just before the output coupling-cap!
As you can see ... these are in phase - so the coupling cap has not added any phase???
Actually, you are both wrong. Although the steady state sine wave current and voltage in a capacitor are 90 degrees apart, a capacitor in a filter causes a continuously varying phase shift with frequency in the output. The 90 degrees comes from I = C x dV/dt
because if V is a sine, then the derivative I is a cosine. The sine and cosine waveforms are 90 degrees apart.
In an RC high pass filter, the phase shift of the transfer function varies from +90 degrees (at low frequency),
to 0 degrees (high frequency asymptote). You choose C for the 0 degrees region to cover the frequencies of interest.
In an RC low pass filter, the phase shift of the transfer function varies from 0 degrees (low frequency asymptote),
to -90 degrees (at high frequency). You choose C for the 0 degrees region to cover the frequencies of interest.
because if V is a sine, then the derivative I is a cosine. The sine and cosine waveforms are 90 degrees apart.
In an RC high pass filter, the phase shift of the transfer function varies from +90 degrees (at low frequency),
to 0 degrees (high frequency asymptote). You choose C for the 0 degrees region to cover the frequencies of interest.
In an RC low pass filter, the phase shift of the transfer function varies from 0 degrees (low frequency asymptote),
to -90 degrees (at high frequency). You choose C for the 0 degrees region to cover the frequencies of interest.
There is always phase shift in an RC type LP or HP filter, although it may be small at frequencies far from the pole.
We are not talking about flipping the polarity, this is a nonlinear phase shift with frequency.
An active inverting stage does not have 180 degrees of phase shift, rather it inverts the polarity of any waveform.
At frequencies well within the RC filter passband, the phase shift approaches a linear phase shift with frequency,
which amounts to a constant time delay, independent of frequency.
This is not true. What is true is that the current through the capacitor and voltage across it are at 90 degrees.
In a typical coupling-cap application the cap's impedance is very much smaller than the load impedance and can pretty much be ignored, so the phase shift is tiny.
A coupling cap forms a voltage divider with the load impedance. The phase shift of a divider is given by arg(Z_load / (Z_load + Z_cap)), for instance with a 1uF capacitor, 10k load impedance and 1kHz, it is 0.9 degrees of phase shift. (And that's a poor coupling cap value, with a high cut-off at 16Hz - 10uF would be a better value for 10k load).
To be clear about the phase response of the RC high pass filter transfer function (series C, shunt R):
T(s) = R / ( R + 1/sC) or rearranged T(s) = SRC / (1 + sRC)
For the steady state frequency domain, s = jω, where ω = 2πf, then T(jω) = jω RC / (1 + jωRC)
and multiplying both top and bottom by the complex conjugate of the denominator, to form real and imaginary terms
T(jω) = jωRC x (1 - jωRC) / (1 + (ωRC)^2) = IM( T(jω) ) + RE( T(jω) )
The phase response is: arctan( IM/RE ) = arctan( (ωRC) / (ωRC)^2 ) = arctan( 1 / ωRC )
This nonlinear phase response curve varies from +90 degrees ( ω -> 0 )
to +45 degrees (ω = 1/RC) which is at the pole
to 0 degrees ( ω -> infinity)
T(s) = R / ( R + 1/sC) or rearranged T(s) = SRC / (1 + sRC)
For the steady state frequency domain, s = jω, where ω = 2πf, then T(jω) = jω RC / (1 + jωRC)
and multiplying both top and bottom by the complex conjugate of the denominator, to form real and imaginary terms
T(jω) = jωRC x (1 - jωRC) / (1 + (ωRC)^2) = IM( T(jω) ) + RE( T(jω) )
The phase response is: arctan( IM/RE ) = arctan( (ωRC) / (ωRC)^2 ) = arctan( 1 / ωRC )
This nonlinear phase response curve varies from +90 degrees ( ω -> 0 )
to +45 degrees (ω = 1/RC) which is at the pole
to 0 degrees ( ω -> infinity)