So far in this series of posts, I have been looking at shaping the loop gain of an amplifier by modifying its forward gain $A$:
Although I only scratched the surface of that topic, let me move to the gain of feedback network $B$."Remember, the whole idea is for you first-timers to get your feet wet in the shallow end of the pool. Put on some sun screen, and come on in. The water's fine." © Nelson Pass 2012
Friday, February 26, 2021
Audio Amplifier Feedback - Lead Compensation
Saturday, February 20, 2021
Audio Amplifier Feedback - LTP with LR compensation
Since my previous post was about shaping the open loop gain of a long-tail pair (LTP) with an RC network across the load, it seems to be a convenient moment to talk about LR compensation of an LTP:
Another potential problem is that the inductor is an effective antenna and will increase inductive coupling of noise from e.g. power supply rails into the LTP. The standard remedy is to use a shielded inductor and/or use two inductors in series connected in anti-phase, so that noise coupled into one is cancelled by the other.
Tuesday, February 16, 2021
Burning Amp BA-3b (Balanced) Updated Power Supply
In my previous post of the Burning Ampifier 3 Balanced, I mentioned that I replaced the CRC filters in the power supply with 100mF + 10mH + 100mF CLC filters per rail per channel. Here are some pictures of the new power supply:
Saturday, February 13, 2021
Audio Amplifier feedback - LTP with Frequency Dependent Load
In a number of previous posts, I looked at shaping the gain of a simple common emitter stage by applying frequency dependent local feedback. Local feedback, however, is not the only available gain-shaping tool. Another commonly used way is to add frequency dependent load.
Consider a simple long tail pair (LTP):
The analysis of the LTP can be found in many places online; my favorite is the ECE 3050 class notes by Marshall Leach. For small signals, the LTP is essentially a voltage dependent current source with transconductance $g_m={1 \over r_e} = {I_E \over V_T} = {I_{LTP} \over {2 V_T}}$ loaded with $R_1$ and $R_2$:
Clearly, by making $R_1+R_2$ frequency dependent, the gain $${v_o \over v_{diff}} = {{v_{C1}-v_{C2}} \over v_{diff}} = {{v_{diff} \times g_m(R_1+R_2)} \over v_{diff}} = g_m(R_1+R_2)$$ can also be made frequency dependent. For example, one can connect an RC network across $R_1+R_2$:
This modifies the load impedance from $R_1+R_2$ to $${(R_1+R_2)||({R_c+{1 \over {s C_c}}})}={(R_1+R_2){{(s R_c C_c+1)} \over {s(R_1+R_2+R_c)C_c+1}}}$$ with a zero at $\omega_z={1 \over {R_c C_c}}$ and a pole at a zero at $\omega_p={1 \over {(R_1+R_2+R_c) C_c}}$.
With the values shown, the zero is at 1.6MHz and the pole is at 2.65kHz (blue trace); for comparison, the green trace shows the response of the same LTP without the RC network:
In principle, the input impedance of the next stage (e.g. a common emitter amplifier) should be included into the calculation as connected in parallel to $R_1$ and/or $R_2$. That does not affect the zero, but the position of the pole can be more difficult to find. Note that the input
impedance of a typical second stage of an audio amplifier with Miller
compensation falls with frequency and can be quite low, pushing the pole
to a higher frequency. This usually is a desirable outcome
as it limits the phase lag introduced by the pole within the amplifier's bandwidth.
If the LTP is loaded not with resistors but with a current mirror, the formulas above still hold if you use the actual load impedance instead of $R_1+R_2$. The load would include the input impedance of the next stage in parallel with the output impedances of the differential pair itself and of the current mirror. For higher load impedance, the pole moves to a lower frequency. At the limit, if the differential pair is a pure current source with infinite output impedance, and the RC network is its only load, the pole appears at $w_z=0$.
Saturday, February 6, 2021
Audio Amplifier Feedback - NCore style compensation
After analyzing the two-pole compensation scheme with the C-R-C "T" network, it became clear that compensating an audio amplifier is not just about ensuring stability, but about shaping (usually maximizing) the loop gain in the audio range of frequencies. This can be achieved in many different ways, and here is another one.
At the 131st AES convention in 2011, Bruno Putzeys presented a paper titled High-Order Analog Control of a Clocked Class-D Audio Amplifier with Global Feedback Using Z-Domain Methods, discussing the details of then-new Class D amplifier technology, marketed by Hypex under the trade name NCore. An NCore amplifier has an analog control loop with five poles, one real plus two complex pairs. One pair comes from the LC output filter, and the others come from the following circuit:
Saturday, January 30, 2021
Audio Amplifier Feedback - Two-Pole Compensation
As I noted in my posts on limitations of dominant pole compensation and on nested loops, dominant pole compensation locks a lot of gain inside the local feedback loop and makes it unavailable to the global feedback loop. The simplest way to unlock (part of) that gain is two-pole compensation.
Two-pole compensation implemented with a C-R-C “T” compensation network is well known since 1980s and was featured in Douglas Self's comprehensive article on frequency compensation in the February 1994 issue of Electronics World - see FIG 1D on the right:
An intuitive explanation of how the C-R-C compensation network works is simple:
- $R_P$ and $C_{P2}$ form a frequency-dependent voltage divider that feeds $C_{P1}$ with a portion of the output voltage
- At low frequencies, the impedance of $C_{P2}$ is high compared to $R_P$, so $C_{P1}$ sees a only a small portion of the output voltage, the local feedback's loop gain is reduced, and more gain is available for the global feedback loop
- At high frequencies, the impedance of $C_{P1}$ and $C_{P2}$ is low compared to $R_P$, so both capacitors in series work as a Miller compensation.
Despite being around for 30+ years and probably because of its simplicity, a formal analysis of two pole compensation was published only in 2010 by Harry Dymond and Phil Mellor from University of Bristol, who presented their paper at the 129th AES convention. A brief summary:
- Similarly to Miller's single dominant pole, the location of the two poles depends on the amplifier's stage inside the local feedback loop
- The zero is located at the frequency $f_z = {1 \over {2 \pi R_P (C_{P1}+C_{P2})}}$
- Unity loop gain frequency is $f_0 = B \times g_m {(C_{P1}+C_{P2}) \over 2 \pi C_{P1} C_{P2}}$, where $B$ is the transfer function of the feedback network and $g_m \approx {1 \over {r_e + R_e}}$ is the transconductance of the input stage
Thursday, January 28, 2021
Velleman K4040 Photo Gallery
Saturday, January 23, 2021
Audio Amplifier Feedback - Transient Intermodulation Distortion (TIM)
Now that I covered the linearity of the input stage, it is a good time to talk about TIM - Transient Intermodulation Distortion.
In 1970, Matti Otala published a paper called "Transient Distortion in Transistorized Audio Power Amplifiers". He argued that under certain conditions, fast signal transients create a specific type of distortion, which he called Transient Intermodulation Distortion (TIM).
In the paper, Otala considered a simple model amplifier with an RC compensation network providing a dominant pole:
Otala fed this model amplifier with a fast voltage step and observed something like this:Here, the green is the step at the input $V_2$, blue is the slower output step, scaled down by the feedback network $\beta$, and red is $V_3$, the difference between the input and scaled output which is fed to the input stage $A_1$.Otala recognized that the overshoot at the input of the first stage may lead to the first stage clipping and thus to distortion - the effect he called Transient Intermodulation Distortion, or TIM.
I demonstrated in the previous post that a difference amplifier typically used as an input stage can easily be overloaded by relatively small signals, and that is becomes nonlinear and start distorting long before it clips. This is one of the mechanisms that potentially can give rise to TIM.
I have been arguing in my first post on audio amplifier feedback that the the difference signal seen by the input stage can be effectively reduced by increasing the loop gain. Indeed, the higher the loop gain is, the smaller both the overshoot and the steady state value of $V_3$ are, and the faster the overshoot settles to the steady state value:
The price of faster settling and smaller overshoot with higher loop gains, however, is the larger current though the RC network, all of which must be provided by the first stage $A_1$:
The extra current required by the compensation network may also lead to the first stage overload, but at the output rather than at the input. This is another mechanism that can potentially generate TIM.
The conclusions should have been that, in order to minimize TIM:
- The slew rate at an amplifier's input should be limited (by, for example, a low pass filter) to what the amplifier can reproduce at the output; and
- The first stage $A_1$ should be designed to both handle the difference input signals and drive the compensation network with low distortion; the now-standard approach (see my previous post) is to degenerate the input differential pair with emitter resistors and increase its tail current.
Otala came to the first conclusion, but not the second. Instead of designing a more robust and linear input stage, he set out to avoid both the overshoot at the input and the need to drive the compensation network at the output of $A_1$ by increasing the amplifier's slew rate, refusing to apply the dominant pole compensation and reducing the loop gain in the global feedback loop.
Importantly, Otala came up with the idea that there is an optimal level of feedback (loop gain), above which TIM would become the dominant distortion mechanism. The theme has become popular and led to the concept that it is the slew rate, and not the loop gain, that determines an amplifier's distortion. It still reverberates around the audio community in the form of amplifiers with "moderate feedback" and slew rates of 3kV per microsecond.
There is nothing wrong with high slew rate amplifiers. For a typical three stage Miller compensated amplifier, the slew rate can be an indication of how far the first stage of the amplifier is from clipping, and therefore how linear it is. It can also be an indication of the amplifier's bandwidth and hence of the loop gain in the audio range of frequencies.
Moderate feedback, on the other hand, is a problem. As I posted earlier, moderate feedback provides only moderate suppression of distortion and makes the input stage work harder and distort more. Conversely, high gain in the global feedback loop reduces the difference input signal for the input stage and thus reduces TIM. There is no need to choose between high loop gain and low TIM; one can - and should - have both.
Saturday, January 16, 2021
Audio Amplifier Feedback - Input Stage Linearity
In my previous posts, I mentioned that dominant pole compensation limits loop gain, which increases distortion in two ways.
- Lower loop gain means that the feedback loop has lower ability to correct distortion as the Error Transfer Function $ETF={1 \over {1 - LG}}$ increases.
- Lower loop gain means the input stage needs to deal with a larger signal.
- One is to make the input stage intrinsically more linear. This usually means making it more complicated or, if the input stage is an opamp, selecting a better (and more expensive) opamp.
- Another is to make the differential input signal smaller by increasing the loop gain.
Sunday, January 10, 2021
Krell KSA-5 Clone - Revised Schematic and Build Guide
In the previous two posts on the topic, I discussed my approach to upgrading the KSA-5 and demonstrated the massive distortion improvement I was able to achieve.
Without further ado, here is the revised schematic:
- 8x 0.22 ohm 2W or 3W resistors
- 4x 22 ohm resistors
- 6x 47 ohm resistors
- 8x 100 ohm resistors
- 8x 274 ohm resistors
- 4x 332 ohm resistors
- 2x 562 ohm resistors (not needed if you can reuse R5/R8)
- 2x 3.92k resistors
- 2x 1 Megohm resistors
- 2x 68pF 50V capacitors, NP0/C0G ceramic or mica
- 4x 4.7nF film capacitors
- Some 18 AWG single core insulated wire and 2x 10 ohm 2-3W resistors for the output RL network
The list of changes to the original schematic:
- Replace R1, R2, R6, R7 with 100 ohm resistors
- Replace R5 and R8 with 332 ohm resistors
- Replace R9, R10, R11, R12 with 274 ohm resistors
- Replace R16 and R17 with 22 ohm resistors
- Replace R19 with a 562 ohm resistor (reuse one of R5/R8)
- Replace R23 with a 1 Megohm resistor
- Replace R24 with a 68pF 50V NP0/C0G ceramic capacitor
- Replace R33, R34, R35 and R36 with 0.22 ohm 2W or 3W resistors
- Replace R37 and R38 with one 47 ohm resistor connected between bases of Q23/Q24 and Q25/26. Make sure to connect the new resistor correctly - see the build guide below - or your output transistors are at risk.
- Replace R47 with a 3.92k resistor
- Remove C2 and C3
- Add a 4.7nF film capacitor and a 47 ohm resistor, connected in series, between the collectors of Q2 and Q3. Add another 4.7nF film capacitor and a 47 ohm resistor, also connected in series, between the collectors of Q7 and Q8. Place the new parts on the underside of the board if you like.
Saturday, January 9, 2021
Audio Amplifier Feedback - Nested Feedback Loops
In the previous post, I looked at how Miller compensation reduces the global loop gain of an amplifier. Where does the gain go? It gets trapped inside the local loop that the compensation capacitor forms around the second (transimpedance) stage.
When several stages are included within one feedback loop, the individual gains of each stage multiply (left). However, when one of the stages is enclosed in a local loop, the contribution of that stage to the global loop gain changes - it becomes the Signal Transfer Function set by that local loop (right).
With Miller compensation, the magnitude of the second stage's Signal Transfer Function falls with frequency by 20dB/decade. Because of that, at low frequencies most of the raw open loop gain of the second stage is applied to the global feedback loop. As the frequency grows, the gain of the second stage is increasingly removed from the global loop and locked inside the local loop.
As discussed in the last post, the decreasing global loop gain affects distortion at high frequencies. The effect is quite dramatic - here is an illustration from Douglas Self's Desiging Audio Power Amplifiers book:
In the next post, I will look into how loop gain affects the linearity of the input stage of an amplifier.