(Raw copy of design notes, not proofread yet, but will be soon)
It shall be assumed a fairly low source resistance (<100 ohm), the main input source shall be assumed iPhone/other smartphones. The preamplifier shall be implemented fully with active circuitry, to preserve the headroom and signal to noise ration.
Input stage/balance control
The input stage is the interface to the outside world, and where the input audio signal is physically connected. The input stage has several tasks.
The input signal is potentially noisy with high frequency (RF) noise. This noise needs to be filtered out as soon as possible, and the first components in the input stage are a small-valued resistor and a small-valued capacitor. These form a low-pass filter to filter out the RF noise.
Two clamping diodes protects the input stage against high voltages.
Buffering and small variable gain (balance control)
An non-inverting opamp amplifier ensures high input impedance. At DC this amplifier operates as a follower. The feedback network however, is arranged as a non-inverting amplifier at signal frequencies, with capacitors C3 and C4. The gain of this amplifier can be set with the potentiometer, and functions as a balance control. The potmeter is a dual potmeter with the terminals wired oppositely, so that the gain can be shifted towards one side or the other. The feedback network must be dimensioned such that it can be driven by the op amp output.
AC input coupling. Need for output coupling to next stage (volume control)? Probably not, bot need control over voltage offset.
The tone control is based on the Baxandall tone control. This is basically an op amp based inverting amplifier, with the feedback network consisting of two separate feedback paths, one for low frequency signals (bass network) and one for high frequency signals (treble network). The gain of each network is controlled by a potentiometer.
The aim is to design treble and bass controls that leave the frequency response flat when adjusted to the middle position. When the control knobs are adjusted clockwise the treble/bass response is boosted, and when adjusted counterclockwise the response is attenuated.
The Baxandall tone control circuit with single capacitor for bass and treble is shown in the figure below.
With both controls set to middle position, the circuit gives a flat response with unity gain (0dB). This is set by the resistors in both the bass treble feedback networks (R1, R2 and R3 in the bass network and R6 in the treble network).
By turning a control knob clockwise (potentiometer viper moved downwards in the figure), the response is boosted (in this case up to about +16dB (6,3 times), as shown in Figur 2. Correspondingly, of turned counterclockwise, the response is attenuated by about 16dB.
A simplified version of the circuit, including only the bass network is shown below.
(In addition the potentiometer R6 will be in parallel with R2, R3||C1 and R1, but will not affect the gain or frequency response, since it is connected directly between input and output. However, it will affect the input impedance)
The figure below shows the bass response for different settings of potentiometer R3.
At low frequencies capacitor C1 is blocking, and the gain is defined by the voltage divider consisting of the potentiometer R3 together with R1 and R2. The upper and lower limit of the gain is set by R1 and R2. With the component values shown the maximum gain will be (10 + 1,8)k/1.8k = 6,56 = 16,3dB, and the minimum gain will be 1,8k/(10 + 1,8) = 0,15 = -16,3dB,
At high frequencies capacitor C1 is functioning as a shortcut, disabling the function of the voltage divider, and the gain is set to unity by R1 and R2. Both the LF anf HF gain can be confirmed from the figure above.
LF Time constants
So what is “high” and “low” frequencies exactly?
The figure below shows the circuit with the potentiometer in the boost position. The corresponding curve in the figure above is the upper bass curve (green). We see from the circuit that capacitor C1 and the potentiometer forms a low-pass filter in the feedback loop of the op amp. This means that the -3dB frequency of the low pass filter defined by the bass network is (approximately) 1/2πC1R3 = 160Hz.
As the frequency increases the gain will asymptotically approach unity because the potentiometer will be gradually shorted by capacitor C1.
[We can find the 3dB frequency from the lower bass curve, which is actually the response of the high-pass filter formed by capacitor C1 and resistor R1, thus 1/2πC1R1 = 884Hz???]
The (simplified) treble circuit is shown in the figure below. Note that the bass potentiometer is shorted by bass capacitor C1 at high frequencies; hence both are omitted from the treble circuit. Also note that the bass potentiometer could have a value between zero and one fourth of its total value (depending on its setting) in series with R4.
The HF gain is a bit more complicated to calculate than the LF gain, since we need to take the bass resistor network into the calculations as well. An equivalent HF circuit with the treble potentiometer boosted is shown below. The treble potentiometer appears directly in parallel between input and output, and does not influence gain or frequency response. However, it does affect input impedance.
The gain can be found by writing node equations at node A and B. Note that node B is virtual ground and is at 0 volt. Also note that one fourth of the bass potentiometer has been added in series with R4 (assuming middle position), that is R4 = 22k + 2,5k = 24,5k.
The gain expression is:
(Remember to account for the bass potentiometer in R4)
Note that in addition to defining the HF gain, R4 also influences on the amount of influence of the bass circuit on the treble response. The larger R4, the less interaction.
For the values shown, the gain is 6,58 (16,4dB), which is consistent with ac and dc simulations.
(Verifiser også at dette er symmetrisk)
HF Time constants
From the treble circuit we see that C2 and R5 appears directly at the input of the op amp. Together with the feedback resistors this is a high-pass filter with time constant R5*C2, with a 3dB frequency of 1/2πC2R5 = 3,7kHz.
R4 defines the relationship with the bass network, and thus the gain of the treble network. How?
Need to calculate:
The volume control is used to adjust the sound level to the desired setting. The human hearing is logaritmic in nature, with a greater sensibility at lower levels. The volume control should reflect this, so that the rotation of the potmeter results in sound level that approximates the logarithmic sensibility of the ear (“Linear in dB”).
In a stereo system it is also important that the volume control affects the two channels equally, so that the left-right balance is not affected by the volume control.
Finally, it is important that the volume control at the lowest settings results in perceived total silence.
A volume control can be as simple as a potmeter wired as resistive voltage divider. Such a passive attenuator creates challenges with signal to noise ratio, headroom bottlenecks, low input impedance and high output impedance. The two last issues can of course be solved by appropriate buffering. But if introducing active circuitry it seems more plausible to exploit it more fully by implementing a fully active volume control.
The challenge of logarithmic law... One option is to use a logarithmic potentiometer. These are, however, very crude aporoximations, usually consisting of two linear segments. The tolerance is normally 20%, which is a potential problem when it comes to channel balance.
Another solution is to try to create a circuit with an approximate logarithmic law using a linear potmeter. A well-known example of this is the Baxandall volume control, which not only approximates a logarithmic relationship, but also eliminates the potmeter track resistance entirely from its transfer function. This removes dependence on the 20% tolerance on the track resistance. The gain's dependence of the potmeter is then given entirely by the position of the viper.
The Baxandall volume control is built around an inverting amplifier in which the gain is defined by R2/R1. This is the maximum gain of the volume control circuit. This inverting amplifier is buffered by a voltage follower circuit.
Around this amplifier with finite gain R2/R1 is another feedback network, also configured as an inverting amplifier. Since feedback circuit cannot have higher gain than the amplifier inside the feedback loop, the maximum gain (with the potmeter at the max setting) of the entire circuit will be R2/R1, as described above. At other potmeter settings the gain will be dependent only of the viper position (x/(1-x), see figure) in addition to R2/R1.
A volume control circuit based on the Baxandall circuit is shown in the figure below.
The max gain is defined by resistors R1 and R2, which with the chosen values give a max gain of 4.7/1.2 = 3.9, or 11.9dB, according to the gain structure in section 2.3.
C1 and C4 are DC blocking capacitors.
C2 prevents the bias current from U1 to enter the potentiometer. DC currents should be avoided in a potentiometer, since this can cause scraping sounds when the viper moves over the track resistance.
R4 is a drain resistor preventing buildup of voltage due to leakage currents in C4.
R5 isolates the stage from load capacitances and helps ensuring stability.
Click to enlarge images below