The Art of Electronics

In the international community, especially in the world of classic electronics, two types of paired transistor topologies are well-known: the Darlington Pair (DP) and the Sziklai Pair (SP, also popular as Complementary Pair ) . However, in electronics education, the DP is far more popular than the SP.  Especially in audio engineering applications, both are used, but the DP remains more common. This popularity may not be because it's inherently better than the SP, but perhaps because many in the electronics community overlook some of the SP's advantages. Generally, as linear power devices, the SP offers several benefits: The SP produces an average Total Harmonic Distortion (THD) that is approximately 1/3 of the THD generated by the DP. Bias stability due to thermal effects in the SP topology is primarily determined by its driver transistor, which is relatively easy to manage (due to its low thermal power). The DP topology has more critical thermal stability because it's de...

The  damping factor (DF)  is a parameter that measures an amplifier's ability to control a speaker's cone movement, especially at low frequencies (bass). Simply put, DF is the 'brake' that prevents a speaker from oscillating excessively after the audio signal stops.  Mathematically, the damping factor is expressed as:  $$ DF = \frac{Z_{speaker}}{Z_{amplifier} + Z_{cable}} $$ Where: $Z_{speaker}​$  : The nominal impedance of the speaker (e.g., 4Ω, 8Ω). $Z_{amplifier​}$ : The output impedance of the amplifier (typically very low, < 0.1Ω). $Z_{cable}$  : The total resistance of the speaker cable. Notes :  In this formula, $Z_{cable}$ does not refer to the Transmission Line Characteristic Impedance, which you might find in RF coax cables (e.g., 50 or 75 ohms). Instead, it represents the true end-to-end impedance—the impedance measured across both ends of the speaker wires, including any filters or crossovers that might be installed. In...

While browse the internet, especially on electronics-related websites, I came across a simple audio amplifier circuit or schematic that uses only three transistors. It seems the designer intended it for low-power speakers, probably just 2 to 3 watts, similar to an extension speaker to boost the audio signal from a laptop, phone, or other audio devices. I took a brief look, and my intuition told me that while the amplifier would likely produce sound at its specified wattage, the distortion would be quite high. I noticed the circuit was a bit unconventional because it used a bias for the power stage that would inevitably fluctuate, even though it was said to be used for limiting overcurrent. In my experience, if that was the goal, it wouldn't work as intended.  However, out of curiosity to see if my intuition was correct, I ran a simulation. And I was right—the circuit's amplification was not linear or symmetrical. For simple **playback**, this might not be an issue, but for audi...

When you're using operational amplifiers (op-amps ) or other linear amplifiers, there's a crucial parameter you should understand: the Gain Bandwidth Product (GBP) . It's the relatively constant product of an amplifier's gain and its bandwidth, and it's a fundamental concept for a solid intuition in electronics. For any linear amplifier, your chosen voltage gain (G)  will dictate the corresponding operational bandwidth (W) . This relationship is fixed by the amplifier's constant GBP. The formula is simple: G x W = GBP The first image shows a typical curve for an amplifier's GBP. You'll notice the gain decreases steadily as the frequency increases. This is a deliberate design choice called frequency compensation , and it's what keeps the amplifier stable. Most linear amplifiers, including op-amps, achieve this with a Miller capacitor  inside the circuit, which creates a single dominant pole in the transfer function. This design gives the amplifier a c...

As we know, all types of transistors have a maximum limit for Vds in MOSFETs and Vce in BJT and IGBTs. This parameter must be carefully considered during design (or when replacing / substituting components). For example, let's look at the end-stage or power stage of a Class D amplifier built with a push-pull configuration using two IRFP054 MOSFETs, as shown in the image. What is the safe voltage for Vpos and Vneg for a push-pull configuration where the transistors have a maximum Vds of 60 volts? In practice and during the design phase, we must always incorporate an operational safety margin. Similarly for transistors, a malfunction could cause Vpos or Vneg to spike above its normal value. A safety margin, in this case, means that even if a supply voltage surge occurs, it will never exceed the maximum Vds value of the MOSFET (or Vce for BJT and IGBT). A commonly used safety margin ranges from 20% to 50%. The larger the safety margin, the lower the probability of damage. In a push-pu...