5. Opamp Examples

Introduction

Where page 4 gives some examples of Tube designs with passive (or active) RIAA filters, on this page I detail my design for Phonoclone and other opamp based RIAA phono preamps.

On this page I want to give some more background based on my experience with building the PhonoClone and GainPre phono amplifiers that were built with opamps. Both Phonoclone and GainPre have hybrid filtering: Part of the RIAA filter is included in the feedback loop and the highest pole is passive in between the first and the second Opamp stage. Of-course the active filtering (or negative feedback) principle is usable for tube projects as well. In fact, the Hounddog amplifier was based on the same principle of feedback. Anyway, I'll describe the principle using opamps.

PhonoClone: a Hybrid RIAA Filter

A combination of partly active filtering and passive filtering is often used when building a phono amp with opamps. I call it the Hybrid RIAA filter, by lack of a better word for now. The RIAA filters for PhonoClone and GainPre are built using this principle. Below is the final (hmm) version of the PhonoClone amplifier . R1, C1 and R_2 are part of the filter in the feedback loop. This filter manages the 50 Hz pole and 500Hz zero. The second filter dealing with the higher frequencies is defined by R3, C3 and Rx. This passive filter makes the 2122Hz (75uSec) pole and the 50kHz zero.

Not really part of the filter, but important to take into account are C4 (audio capacitor to avoid DC offset) and R6. Especially C4 must be chosen with care, as a value too low will block the lower frequencies. On the other hand, high values for audiocapacitors do sound less open in my opinion (experience). C0 is of similar importance to keep DC out, but in a next version of this amp I would omit this capacitor since it's function is also provided by C4.

Simplified Model for designing your amp

Figure 5.1 is the simplified figure for the PhonoClone project, and I will use this schematic in the remainder of this section to work with (please mark the new reference designators/numbering of the components). The formulas for the Hybrid variant can be easily derived from the active filter formulas on page 3 (and below).

OK, but now the other way around: Spreadsheets and formulas are goods tools to check the corrrectness of a design, but how can we design our own amp?

Below is a template for designing your own hybrid phono amp. By following it step by step will result in a complete amp with the same layout as phonoclone but with component values of your choice. Given the limited amount of components needed besides the opamps, I do recommend to use high-quality resistors and 1% capacitors in the filter and high-quality audio capacitors for coupling both stages.

Compute Step	Description	Example
	Start with a value for R0. Since I used the AD797 and found it to be unstable for higher values I decided to take a low value of 20 Ohms. Also, in order to minimise offset currents etc. it is a good idea to load the positive and negative input of the opamp more or less equally. And since I designed this amp primarily for MC cartridges with a load of 10-100 Ohms... (Should I design this amp again, there is a big chance that I'll use active step-up amplification with FET instead and use this design for MM-level amplification)	20 Ohm
	Decide on your amplification factor for the first stage. Since the RIAA filter is placed between the first and the second stage, the first stage must have sufficient gain in order to deal with a reduction of gain for higher frequencies of 20kHz. I decided to go for a gain of about 46 dB (200 times) in the first amp stage. We have to, since the RIAA filter will not reduce gain at 20Hz, but at 1kHz it will reduce gain with about 19.2 dB and at the 20kHz point with another 19.6dB. Anyway, there will be some amplification left, and it is recommended to start with a gain of at least 45dB.	46 dB = 200
	As we want a gain of at least 160, the value of R1 needed to be around 3.3kOhm. I decided to go for a capacitor of 1uF and therefore I choose R1 as 3300 Ohms (according to the formula 3180 would have been better).	3300 Ohm
	For the first pole of the RIAA curve at 3180 uSec, R1 C1 * w = 1. As defined on the first page, w = f 2 * pi(), and the time constant equals 1/w. And therefore R1 * C1 = 3180. Round C1 to the nearest standard value and then goto step 5, or put some caps in parallel in order to exact match the ideal value for C1 by given R1, in this case goto step 7
	Optional: If C1 is rounded and differs from the exact value, we have to recalculate R1, and maybe find a closer value now C1 is fixed.
	Optional: Recalculate R0 for the chosen value of C1 (which might differ from the exact computed value)
	For the 500Hz zero point on the curve, we use the formula on page 3: R2 = R1/ 9 - R0. Since C1 has already been chosen as 1uF (1e-6F) and 1/w and R1 and R0 are chosen as well. Resolving R2 from this equation gives R2 = 345 (which I rounded to 330 Ohm).	330 Ohm
	Next we have to choose a value for C3 as it determines both the value for R3 and Rx. In general it is good to choose a value in between 10nF and 50nF. I chose C3 to be 33nF.	33 nF
	Next we need to compute the value of Rx, for the optional timeconstant t4 of the RIAA curve with a zero at 50,000 Hz. The value of Rx can be computer using the formula C3 * Rx = 1/w = 3.18e-6, and since we have chosen C3 above, Rx can be computed: 96.5 Ohms. (remark: During simulations it appears that the value is too high and will cause higher frequencies to rise faster than desired. I used a value of 10 Ohms for Phonoclone).	90 Ohm
	Now we can to calculate the value for R3. In this case (R3+Rx) * C3 = w(2122Hz) = 75 uSec, and since we choose C3 and computed/choose Rx above, R3 can be computed as (75e-6 / 33e-9) - 10= 2263 Ohm. In order to use standard values, we choose it to be 2400 Ohms (but remember the 2263, cause we need it later).	2400 Ohm
	Not found in the simplified figure 5.1 above, but needed in the real phonoclone design are the audio capacitor C4 and a grounding resistor R6 to the input of the next amplifier stage. Resistor R6 will be chosen such that the error we made when rounding R3 will be as small as possible. Because R6 and R3 are parallel to capacitor C3, we can use the formula for parallel impedances: 1/2263 must be equal to 1/2400 + 1/R6. Using your favourite calculator this means that R6 should be around 39k (I choose 43k because at first I did not use resistor Rx, looking back, 39K would probably have made more sense)	39 kOhm
	For the value of the coupling capacitor I have chosen a value of 1 uF so that the lower frequencies will all make it to the next amplifier stage. The value can be computed as follows: 1/ ( 2 * pi() * rolloff_freq * (R3 + R6 ) ) = 1 / (2pi() 5 * ( 2400 + 43000 )) = 0.7 uF (minimum)	1 uF
	Decide on your gain for the second stage, if the total gain of the Phono amp needs to be 50 dB, than substract from this number the gain of the first stage.
	In phonoclone I used a value of 20 Ohms in order to keep the opamp stable, but normally a value of 1kOhm would do just fine and prevents excessive current.	20

	For the sake of completeness, I did include C0 on this page. I do however recommend that you try to build your amp without C0 as it's function is duplicated from C4 anyway.

I have a spreadsheet available for the design template described above. Email me your experience with the spreadsheet.

Gain Formulas

In this paragraph I'll work out the gain formula's for the passive and the active part of the filter. The background of these formulas has been explained on page 2 (passive) and page 3 (active designs) and therefore, we'll use the formulas in a fast and simpler form. Formula 5.1 defines the first -active- half of the Hybrid filter. In spreadsheet simulations of formula 5.1 it is clearly shown that the first pole and zero are correctly implemented and that the curve starts to deviate at the next pole of 2122 Hz (see blue line in chart below).

Not part (yet) of the model, but equally important is the output impedance of the Opamp V1, which of course needs to be added to the resistor R2 for correct results. For larger values of R1 and R2 this will not play any significant role, but for PhonoClone with its resistor value of 330 Ohms it is good to take the output of V1 into consideration. For opamps, the open loop output resistance is typically between 55 and 70 Ohms.

OK, lets have a look at the second part of the filter, the passive part. The passive part of the filter is very straightforward and easy to use in calculations. Compare the formula below to the RIAA formulas on page 1 and it is easy to see the relationship between C3, R3, Rx and the corresponding time constants of the RIAA curve.

The formula above is defined on one the previous pages (passive RIAA) and can be used to combine with the formula's for active filtering on this page to get a complete RIAA network.

Therefore, I entered both the passive and the active formulas in a spreadsheet and calculated the resulting deviations from the ideal RIAA curve for each one separately. After that, the two formula's were combined (and adjusted for the ideal RIAA curve) and the resulting values were be plotted in a chart found below. Keeping in mind that the full phonoclone design includes an audio capacitor and some other components and the SPICE models do take into account the output impedance of opamps, the deviation from the RIAA curve in this example (about 0.5dB) is therefore understandable.

PhonoCard: Inverted Design, Active Filter

Early in 2003 the phonocard started, but after designing a first prototype I was so much involved in my other projects that the phonocard project came to a standstill. That was until someone opened a topic on diyaudio.com on this subject. The feedback I received made me decide to finish the project.

I also received feedback from Werner Ogiers and Thorsten Loesch regarding the design itself. The plans were already to build the phonocard with two inverted sections, but Thorsten told me that active feedback filters do sound better with OpAmps than passive. As I did not build such an amp yet, since based on my experience with tube amps I would have used a passive filter here, I decided to rework the design and build one with an ative RIAA filter (feedback).

The RIAA filter is split over the two amplifier sections. Both are inverted.

Please have a look on page 3, figure 3.3 and formula 3.2 and the formula 5.1 above. Roughly the same formula's do apply in a non-inverted configuration, only the gain of an inverted configuration is not 1+(Rfb/Ri) but -Rfb/Ri. Therefore, the total formula for the active filter (as in each of the sections of Phonocard) is as follows:

For two sections of the amp, each with a part of the RIAA filter, we have to multiply the gain formulas or in this case add up the dB values in order to describe the total phono amp.

From the formulas above it's relatively easy to compute the ideal values for the components in both active filters based upon the following equations. When rounding these ideal values to standard E96-range of resistors it is possible to build a phono amp that is within 0.1dB of the RIAA curve.

And finally, based upon the formula above it's easy to describe a template for building your own Phonocard "clone". The following table defines the template for building your own amp:

Compute Step	Description	Example
	Determine Ri, the DC resistance for your MC cartridge. Usually this is a value between 10 and 50 Ohms. Do not use a multimeter, as this will permanently damage your cartridge. Look it up in the user manual instead.	38 Ohm
	Decide on your amplification factor for the first stage. Since the RIAA filter in the first stage deals with breakpoints 50 and 500Hz, the first stage must have sufficient gain in order to deal with a reduction of gain of 19.2 dB (9.2 times) from 20-1000 Hz. I decided to go for a gain of about 70 (36.9) in the first amp stage at 1kHz, which means that at DC the gain even is 19.2 dB higher.	gain 70 = 36.9 dB, @ 1kHz => 56 dB = 630 @ DC
	Calculate the best value for R1 based on the desired gain. In my case 70 * 9.2 * 38 = 24k47 which I'll round to 24k	24k
	For the first pole of the RIAA curve at 3180 uSec, R1 C1 * w = 1. As defined on the first page, w = f 2 * pi(), and the time constant equals 1/w. And therefore R1 * C1 = 3180e-6. Round C1 to the nearest standard value and then goto step 5, or put some caps in parallel in order to exact match the ideal value for C1 by given R1, in this case goto step 7
	As there are more resistor values than standard capacitor values, recalculate R1 based on the chosen capacitor value/
	In order to keep the gain for the first stage, recalc Ri to see if it is not terribly off. Not that you can change Ri yourself though. If you're not satisfied with the gain, redo some of the steps above.
	For the 500Hz zero point on the curve, we use the formula on page 3: R2 = R1/ 9 for inverted amps. Since C1 has already been chosen and 1/w and R1 and Ri are known as well. Resolving R2 from this equation gives R2.
	Th gain of the second stage is determined by taking the desired total gain and substract the gain for the first stage (step 1). The desired input impedance for Opamp 2 is determined by the OpAmp. The AD797 does not like low impedance inputs, the OPA 637 does not really care. A value of 2k would be nice.	R3 = 2k
	The value of R4 results from the total gain and the value chosen for R3.
	We determine the value for C2 as follows: First calculate the best value for given R4, then choose a value close to that value which is makeable with standard caps and then re-adjust R4 based on that value (there are more std resistor values than cap values).
	So recalculate R4 based on the chosen capacitor value for C2 (C2 may be a standard value or a value composed of several standard caps).
	The value of R5 is related to the value of R4 and the relation between the two time constants t3 and t4 for this specific pole-zero filter.
	Determine the roll-off point for a coupling capacitor on the output based on the roll-off frequency and the impedance resistor at the output (take also imput impedance of the volume pot of your preamp/power amp into account). Normally, 0.47uF-1uF should be fine.	Freq=5Hz, impedance about 50kOhms