In Part 2, we obtained the closed-loop transfer function, and analyzed bandwidth and step response. In this part, we will continue analyzing other dynamic behaviors.

 

Nonlinearity

So far, we have only been analyzing the system using a linear model. However, the LED of the optocoupler is a very non-linear component. As we mentioned before, the LED’s Rb is 3.469 Ω. That means a R3 ≫ 3.469 will make the relationship between VOUT and IOUT much more linear.

Fig. 9 compares the harmonics at R3 = 3.469 + 0, +10, +100, and + 1000 Ω. C1 was chosen in a way so that system’s frequency response are almost all the same at different R3 to make an apple to apple comparison, as shown in Fig. 10. R1 was kept at 100KΩ. Op Amp’s GBW was 500MHz all the time.

Fig. 9 harmonics at different R3

As shown the in plots, with R3’s increase, the 2nd order harmonic is reduced by about 30dB. Here is another tradeoff: higher linearity means higher R3, which inevitably lowers the bandwidth significantly. But the good side is, this also means a higher damping coefficient, resulting less overshooting.

Fig. 10 frequency response at different R3 C1 combinations

 

THD + N (%)

In this session, we take resistors and Op Amp’s noise and harmonics into consideration. How do we design the system with low THD + N (%) with the presence of non-ideal components?

Noise from R1 adds directly to the system’s input. A larger R1 adds larger thermal noise. Also, the photodiodes noise currents are amplified by R1. This seems to suggest a small R1 is good for reducing noise. However, before an Op Amp saturates, its THD + N (%) decrease with signal’s amplitude [4]. That means a large VIN, which translates to a large R1 at the same output current, may reduce the system’s THD + N (%). Then how do we choose R1 to optimize the system’s THD + N(%) performance?

To answer this question, we express the THD + N(%) referenced to Op Amp’s input as

Where VIN_N is the harmonics, VOP_n is the amplifier's input referred noise, 4KTR1 represents the thermal noise from R1, and IPD1_n and IPD2_n are the noise current from the photodiodes. ILED_n is the LED’s noise current, and 4KT/R3 is R3’s thermal noise current. Kopto is the optocoupler’s current gain.

With VIN / R1 = IOUT

We have

This shows THD+N(%) decreases with VIN increase even though R1’s increase introduces more noise. This is because the noises introduced by R1 don’t increase faster than R1’s value while some noises remain independent of R1. In conclusion, a large R1 is good for stability, bandwidth and THD+N(%).


PSRR

If there is noise on Vcc that bias the LED, it will be add to VOUT because Vcc is in series with VOUT. Though the feedback will desensitize the system from the Vcc’s variation, it is still desirable to make it stable at the first place.

One way to alleviate this issue is to bias the LED using ground instead of Vcc, as shown in Fig. 11.

Fig. 11 LED biased at ground

However, the tradeoff is that we lose more than half of the Op Amp’s output swing. This limits R3’s choices, and output swing. There is a way to partially cancel the differential mode noise from power rails, and sacrifice less Op Amp’s output swing. Fig. 12 illustrates the idea.

Fig. 12 bias LED from both Vcc and Vee

In Fig. 12, when R3a = R3b = 2R3, it is equivalent to the network in Fig. 11. However, if we use different values of R3a and R3b, it allows us to bias the anode of the LED to any potential between Vcc and Vee. The closer the potential is to ground, the better the suppression to differential mode power rails noise at the price of smaller Op Amp swing range.

The same technic can be also used to bias LED’s cathode to a voltage that yields better performance of the proceeding Op Amp. This can be useful in cases such as the Op Amp exhibits different THD at different output DC levels.

To use the transfer functions developed previously, replace R3 with R3a // R3b.

 

Other Design Considerations

Op Amp’s input bias current

This is a μA level application. Therefore, to avoid DC offset, it is critical to use an Op Amp of small input bias current. However, Op Amps of small input bias current may not offer the bandwidth or slew rate we desire sometimes. In that case, we can add an extra bias at Op Amp’s negative input to offset its bias current. However, we should bear in mind that this can add extra noise from both the extra source and extra components. This again shows a tradeoff between noise and bandwidth.

R1 Selection

As we mentioned before, it is beneficial to use a large R1 for multiple reasons: stability, THD+N (%), and bandwidth. However, large value resistors often come with larger parasitic capacitance. Fig. 13 shows Yageo’s 0402 SCR027 chip resistor’s impedance as a function of frequency as an example.

Fig. 13 Impedance as a function of frequency for a chip resistor

To alleviate this issue, we can use multiple resistors in series to achieve a high value. This also has a side benefit: it can reduce the 1/f noise from R1.

Layout considerations

Since this is a low current application, and can also work to tens of MHz, it is critical to layout the PCB carefully to guide and constrain the current. It is recommended star-connecting Op Amp’s decoupling capacitors’ grounds and LED’s decoupling capacitors’ ground. This creates a low impedance path for the high current from LED and Op Amp, and prevents it from disturbing photodiode’s currents. PD1’s anode should route to VIN output capacitor before shunting to ground. This can minimize the interference from other ground current to the small photonic current.

Don’t pour copper under the resistors forming R1, because R1 is big and even small the parasitic capacitance can form low pass filter.

All the traces length should be kept short. Decoupling caps should be close to chips.

 

Experiment

A high bandwidth (>5MHz) optical system was built. Fig. 14 shows the system diagram and components values.

Fig. 14 Experimental circuit diagram

Note that the measurement was done at Vo instead of at PD2’s current. For bandwidth measurement, Vin = 2.5V + 2Vsin(ωt). Fig. 15 and 16 shows the bandwidth and step response measurement results

Fig. 15 bandwidth measurement

(a)

(b)

Fig. 16 step responses

The results show that the system had a -3dB bandwidth of 5.5 MHz with moderate peaking. The transmitter’s bandwidth is actually more than that, for the receiver has a bandwidth of 14.4 MHz. The step response’s rising time (10% to 90%) was less than 100 ns, overshoot was less than 5%.

 

Summary

This article gave detailed analysis and design procedures for a μA current source using HCNR200/201 optocoupler. Dynamic performance including stability, bandwidth, step response, non-linearity, noise, and PSRR were discussed in details.

The circuit can be stabilized using only one feedback capacitor, even though the system has two poles. With proper chosen components, the bandwidth of the current source can be extended to much higher than the optocoupler’s own bandwidth. However, a high bandwidth design often results in peaking at the pole, or ringing in its step response. A slightly larger feedback resistor can effectively alleviate this issue, with moderate sacrifice of bandwidth. If a high bandwidth has to be maintained, an Op Amp of much higher GBW will have to be used to suppress the ringing. There is a direct tradeoff between bandwidth and non-linearity. A large resistor in series with the LED can linearize the optocoupler’s transfer function, but also lowers the bandwidth significantly. A large input resistor should be used for the sake of bandwidth, noise, and stability. Finally, PSRR can be improved by changing the DC bias voltage of the LED at the price of limiting the system’s swing.

 

  

References:

[1] HCNR200/201 Datasheet

[3] A Method for Obtaining the Transfer Function of Inverting and Non-inverting Op-amp Circuits Based on Classical Feedback Theory, N.F. Macia, V. O. Blackledge, American Society for Engineering Education Annual Conference & Exposition, 2001

[4] Understanding Harmonic Distortion versus Amplitude in Operational Amplifiers, Jorge Vega, Planet Analog, 6/7/2013

 

Also see:

 

Yong Liao is a Sr. Test/HW Engineer at Broadcom with an MSEE.

Xi Cheng is an R&D Test Engineer at Broadcom, with an MSEE and a physics PhD.

 

 

 

Article originally published on EDN.com.